ThinkCAT Logo
ThinkCAT
Geometry • Triangles & Trigonometry Practice Drills (113 Qs)• Official Answer Keys

CAT Triangles Geometry Practice Questions (110+ Questions)

Similarity & Congruence, Sine/Cosine Rules, Medians, Altitudes, Centroid Properties, and Area Formulas

113 Total Questions
MCQ: 96 (+3 / -1)
TITA: 17 (0 Negative Penalty)
Launch Triangles & Trigonometry Practice Drills Drill in Study ModeInteractive Practice (5,200+ Qs)

Core Formulas & Shortcut Matrix: Triangles & Trigonometry Practice Drills

Cosine RuleFormula #1
\cos A = b2+c2−a22bc\frac{b^2 + c^2 - a^2}{2bc}$

Used to find unknown sides or angles in non-right-angled triangles.

Angle Bisector TheoremFormula #2
ABAC=BDDC\frac{AB}{AC} = \frac{BD}{DC}

Interior angle bisector divides opposite side in ratio of adjacent sides.

Exam Hall Traps & Speedbreakers to Avoid
  • •Confusing centroid (2:1 ratio of median) with orthocenter or circumcenter.

Bite-Sized Practice Sets (12 Modules Available)

Authentic CAT Blueprint

Solve in structured 20–25 question practice sets with instant accuracy benchmarking and solution checks. Sets 01 & 02 are completely free.

13 QuestionsFree Pass

Set 01: Triangles

Difficulty: Easy
Start Free Set
9 QuestionsPro Pass

Set 02: Triangles

Difficulty: Hard
Unlock Set (Pro)
7 QuestionsPro Pass

Set 03: Triangles

Difficulty: Moderate
Unlock Set (Pro)
12 QuestionsPro Pass

Set 04: Triangles

Difficulty: Hard
Unlock Set (Pro)
7 QuestionsPro Pass

Set 05: Triangles

Difficulty: Easy
Unlock Set (Pro)
9 QuestionsPro Pass

Set 06: Triangles

Difficulty: Easy
Unlock Set (Pro)
12 QuestionsPro Pass

Set 07: Triangles

Difficulty: Easy
Unlock Set (Pro)
13 QuestionsPro Pass

Set 08: Triangles

Difficulty: Moderate
Unlock Set (Pro)
9 QuestionsPro Pass

Set 09: Triangles

Difficulty: Easy
Unlock Set (Pro)
7 QuestionsPro Pass

Set 10: Triangles

Difficulty: Easy
Unlock Set (Pro)
8 QuestionsPro Pass

Set 11: Triangles

Difficulty: Moderate
Unlock Set (Pro)
7 QuestionsPro Pass

Set 12: Triangles

Difficulty: Hard
Unlock Set (Pro)
Exam Hall Replica

Attempt under official TCS iON 40-Min countdown timer

Experience real test pressure with on-screen virtual calculator, section lockouts, 5-color question palette, and percentile estimation curve.

Launch Mock Simulator

Official Exam Questions & Explanations (25 of 113)

Sorted in official convenor sequence
Question 1 of 113
ThinkCAT Practice SetQAGeometry • TrianglesEasy
In △ABC,if\triangle ABC , if\angle A = 60∘60^\circ$$ and $\angle B = 70∘70^\circ , what is $\angle C$?
Practice More Questions
Official Correct Answer: A. Using the angle sum property of a triangle, $\angle A + \angle B + \angle C = 180^\circ$. So, $60^\circ + 70^\circ + \angle C = 180^\circ$. Solving for $\angle C$ gives $\angle C = 50^\circ$. Hence, the correct answer is A.
Question 2 of 113
ThinkCAT Practice SetQAGeometry • TrianglesModerate
In $\triangle ABC , the lengths of sides $AB = 6cm,cm,BC = 8$ cm, and $AC = 10$ cm. What is the area of $\triangle ABC$?
Practice More Questions
Official Correct Answer: A. This is a right-angled triangle (since6^2 + 8^2 = 10^2). The area of a right-angled triangle is given by $\frac{1}{2} \times \text{base} \times \text{height}$. So, the area is $\frac{1}{2} \times 6 \times 8 = 24 \text{ cm}^2$. Hence, the correct answer is A.
Question 3 of 113
ThinkCAT Practice SetQAGeometry • TrianglesHard
In △ABC,∠A=90∘,AB=12\triangle ABC , \angle A = 90^\circ , AB = 12 cm, and BC=15BC = 15 cm. What is the length of ACAC?
Practice More Questions
Official Correct Answer: A. Using the Pythagorean theorem, $AC^2 = BC^2 - AB^2 = 15^2 - 12^2 = 225 - 144 = 81$. So, $AC = \sqrt{81} = 9$ cm. Hence, the correct answer is A.
Question 4 of 113
ThinkCAT Practice SetQAGeometry • TrianglesEasy
In △ABC,if\triangle ABC , if\angle A = \angle B = 45∘45^\circ , what type of triangle is △ABC\triangle ABC?
Practice More Questions
Official Correct Answer: B. Since $\angle A = \angle B = 45^\circ , the third angle $\angle C$ must be $90^\circ$ (sum of angles in a triangle is180^\circ). However, the triangle is isosceles because two angles are equal. Hence, the correct answer is B.
Question 5 of 113
ThinkCAT Practice SetQAGeometry • TrianglesModerate
In △ABC,if\triangle ABC , if\angle A = 30∘30^\circ$$ and $\angle B = 60∘60^\circ , what is $\angle C$?
Practice More Questions
Official Correct Answer: B. Using the angle sum property of a triangle, $\angle A + \angle B + \angle C = 180^\circ$. So, $30^\circ + 60^\circ + \angle C = 180^\circ$. Solving for $\angle C$ gives $\angle C = 90^\circ$. Hence, the correct answer is B.
Question 6 of 113
ThinkCAT Practice SetQAGeometry • TrianglesHard
In △ABC,AB=13\triangle ABC , AB = 13 cm, BC=14BC = 14 cm, and AC=15AC = 15 cm. What is the area of △ABC\triangle ABC?
Practice More Questions
Official Correct Answer: A. Using Heron's formula, the semi-perimeter $s = \frac{13 + 14 + 15}{2} = 21$ cm. The area is $\sqrt{s(s-a)(s-b)(s-c)} = \sqrt{21(21-13)(21-14)(21-15)} = \sqrt{21 \cdot 8 \cdot 7 \cdot 6} = \sqrt{7056} = 84$ cm$^2$. Hence, the correct answer is A.
Question 7 of 113
ThinkCAT Practice SetQAGeometry • TrianglesEasy
In △ABC,if\triangle ABC , if\angle A = 90∘90^\circ , AB = 6$ cm, and $BC = 10$ cm, what is the length of $AC$?
TITA Answer:
Practice More Questions
Official Correct Answer: 8. Using the Pythagorean theorem, $AC^2 = BC^2 - AB^2 = 10^2 - 6^2 = 100 - 36 = 64$. So, $AC = \sqrt{64} = 8$ cm. Hence, the correct answer is 8.
Question 8 of 113
ThinkCAT Practice SetQAGeometry • TrianglesEasy
In triangle ABC, if AB = 5 cm, BC = 12 cm, and AC = 13 cm, what is the type of triangle ABC?
Practice More Questions
Official Correct Answer: C. By Pythagoras theorem, $5^2 + 12^2 = 25 + 144 = 169 = 13^2$. Hence, triangle ABC is a right-angled triangle.
Question 9 of 113
ThinkCAT Practice SetQAGeometry • TrianglesModerate
In triangle DEF, DE = 6, EF = 8, and DF = 10. What is the area of triangle DEF?
Practice More Questions
Official Correct Answer: A. Since $6^2 + 8^2 = 10^2 , triangle DEF is a right-angled triangle. The area is $0.5 \times 6 \times 8 = 24$.
Question 10 of 113
ThinkCAT Practice SetQAGeometry • TrianglesHard
In triangle GHI, if the angles are in the ratio 2:3:5, what is the measure of the largest angle?
Practice More Questions
Official Correct Answer: C. The sum of the angles in a triangle is 180 degrees. Let the angles be $2x, 3x, 5x$. Then $2x + 3x + 5x = 180 \Rightarrow 10x = 180 \Rightarrow x = 18$. The largest angle is $5x = 5 \times 18 = 90$ degrees.
Question 11 of 113
ThinkCAT Practice SetQAGeometry • TrianglesEasy
If the sides of a triangle are 5, 12, and 13, what is the area of the triangle?
TITA Answer:
Practice More Questions
Official Correct Answer: 30. The sides form a Pythagorean triplet, so the triangle is right-angled. The area is $0.5 \times 5 \times 12 = 30$ square units.
Question 12 of 113
ThinkCAT Practice SetQAGeometry • TrianglesModerate
In triangle JKL, if the angles are in the ratio 1:2:3, what is the measure of the largest angle?
Practice More Questions
Official Correct Answer: C. The sum of the angles in a triangle is 180 degrees. Let the angles be $x, 2x, 3x$. Then $x + 2x + 3x = 180 \Rightarrow 6x = 180 \Rightarrow x = 30$. The largest angle is $3x = 90$ degrees.
Question 13 of 113
ThinkCAT Practice SetQAGeometry • TrianglesHard
In triangle MNO, the sides are in the ratio 3:4:5. If the shortest side is 6 units, what is the length of the hypotenuse?
Practice More Questions
Official Correct Answer: C. The sides are in the ratio 3:4:5. If the shortest side is 6 units, the sides are 6, 8, and 10 units. The hypotenuse is 10 units.
Question 14 of 113
ThinkCAT Practice SetQAGeometry • TrianglesHard
In △ABC,if\triangle ABC , if\angle A = 30∘30^\circ , \angle B = 2\angle C$ and $AB = 10 , find ACAC.
Practice More Questions
Official Correct Answer: A. Using the angle sum property, $\angle A + \angle B + \angle C = 180^\circ \Rightarrow 30^\circ + 2\angle C + \angle C = 180^\circ$ \Rightarrow 3\angle C = 150^\circ$ \Rightarrow \angle C = 50^\circ$. Thus, $\angle B = 100^\circ$. Applying the Law of Sines, $\frac{AB}{\sin C} = \frac{AC}{\sin B} \Rightarrow \frac{10}{\sin $50^\circ$} = \frac{AC}{\sin $100^\circ$}$. Since $\sin $100^\circ = \sin 80^\circ , and $\sin $80^\circ = \cos 10^\circ , we get $AC = 10 \cdot $\frac{\cos $10^\circ$}{\sin $50^\circ$} = 5\sqrt{3}$.
Question 15 of 113
ThinkCAT Practice SetQAGeometry • TrianglesHard
In △DEF,if\triangle DEF , if\angle D = 90∘90^\circ , DE = 3 , DF = 4 , and $EF = 5 , find the area of the triangle plus the area of the square on $EF$.
Practice More Questions
Official Correct Answer: B. Area of $\triangle DEF = \frac{1}{2} \cdot DE \cdot DF = \frac{1}{2} \cdot 3 \cdot 4 = 6$. Area of the square on $EF = 5^2 = 25$. Total area = 6 + 25 = 20$.
Question 16 of 113
ThinkCAT Practice SetQAGeometry • TrianglesHard
In △GHI,if\triangle GHI , if\angle G = 60∘60^\circ , \angle H = 80∘80^\circ , and GH=10,findGH = 10 , findHI$ using the Law of Sines.
Practice More Questions
Official Correct Answer: A. Using the angle sum property, $\angle I = 40^\circ$. Applying the Law of Sines, $\frac{GH}{\sin I} = \frac{HI}{\sin G} \Rightarrow \frac{10}{\sin $40^\circ$} = \frac{HI}{\sin $60^\circ$}$. Since $\sin $60^\circ = \frac{$\sqrt{3}}{2} , we get $HI = 10 \cdot \frac{\frac{$\sqrt{3}}{2}}{\sin $40^\circ$} = 10\sqrt{3}$.
Question 17 of 113
ThinkCAT Practice SetQAGeometry • TrianglesHard
In △PQR,if\triangle PQR , if\angle P = 30∘30^\circ , \angle Q = 60∘60^\circ , and $PR = 10 , find the length of $QR$.
Practice More Questions
Official Correct Answer: A. Using the angle sum property, $\angle R = 90^\circ$. Applying the Law of Sines, $\frac{PR}{\sin Q} = \frac{QR}{\sin P} \Rightarrow \frac{10}{\sin $60^\circ$} = \frac{QR}{\sin $30^\circ$}$. Since $\sin $60^\circ = \frac{$\sqrt{3}}{2}$ and $\sin $30^\circ = \frac{1}{2} , we get $QR = 10 \cdot \frac{$\frac{1}{2}}{\frac{$\sqrt{3}}{2}} = 5\sqrt{3}$.
Question 18 of 113
ThinkCAT Practice SetQAGeometry • TrianglesHard
In △WXY,if\triangle WXY , if\angle W = 30∘30^\circ , \angle X = 90∘90^\circ , and $WX = 6 , find the length of $XY$. Give your answer as a decimal rounded to 2 decimal places.
TITA Answer:
Practice More Questions
Official Correct Answer: 6.00. Using the angle sum property, $\angle Y = 60^\circ$. Applying the Pythagorean theorem, $XY^2 + WX^2 = WY^2 \Rightarrow XY^2 + 6^2 = WY^2$. Since $\angle X = 90^\circ , WY = \frac{WX}{\cos $60^\circ$} = \frac{6}{0.5} = 12$. Thus, $XY^2 + 36 = 144 \Rightarrow XY^2 = 108 \Rightarrow XY = \sqrt{108} = 10.39$. Rounded to 2 decimal places, $XY = 10.39$.
Question 19 of 113
ThinkCAT Practice SetQAGeometry • TrianglesHard
In $\triangle ABC , the lengths of the sides are $AB = 13 , BC = 14 , and CA=15CA = 15. What is the area of △ABC\triangle ABC?
Practice More Questions
Official Correct Answer: A. Using Heron's formula, $s = \frac{13 + 14 + 15}{2} = 21$. The area is $\sqrt{21(21-13)(21-14)(21-15)} = \sqrt{21 \times 8 \times 7 \times 6} = 84$.
Question 20 of 113
ThinkCAT Practice SetQAGeometry • TrianglesHard
In $\triangle ABC , the median $AM$ is drawn from $A$ to the midpoint $M$ of $BC.If. IfAB = 10$ and $AC = 12 , and the area of △AMB\triangle AMB is $20 , what is the area of $\triangle ABC$?
Practice More Questions
Official Correct Answer: B. Since $M$ is the midpoint of $BC , \triangle AMB$ and $\triangle AMC$ have equal areas. Thus, the area of $\triangle ABC$ is $2 \times 20 = 40$. However, the median divides the triangle into two triangles of equal area, so the total area of $\triangle ABC$ is $48$.
Question 21 of 113
ThinkCAT Practice SetQAGeometry • TrianglesHard
In $\triangle ABC , the angle bisector of $\angle AintersectsintersectsBCatatD.If. IfAB = 12 , AC = 16 , and BD=9,findBD = 9 , findDC$.
Practice More Questions
Official Correct Answer: C. By the Angle Bisector Theorem, $\frac{AB}{AC} = \frac{BD}{DC}$. So, $\frac{12}{16} = \frac{9}{DC}$. Solving, we get $DC = \frac{9 \times 16}{12} = 12 \times $\frac{4}{12} = 8$.
Question 22 of 113
ThinkCAT Practice SetQAGeometry • TrianglesHard
In $\triangle ABC , the lengths of the sides are $AB = 7 , BC = 8 , and CA=9CA = 9. Find the radius of the inscribed circle.
TITA Answer:
Practice More Questions
Official Correct Answer: 2.11. The radius of the inscribed circle is given by $r = \frac{A}{s} , where $A$ is the area of the triangle and $s$ is the semi-perimeter. The semi-perimeter $s = \frac{7 + 8 + 9}{2} = 12$. The area $A = \sqrt{12(12-7)(12-8)(12-9)} = \sqrt{12 \times 5 \times 4 \times 3} = \sqrt{720}$ \approx 26.83$. So, $r = \frac{26.83}{12} \approx 2.24$. Correct to two decimal places, $r = 2.11$.
Question 23 of 113
ThinkCAT Practice SetQAGeometry • TrianglesModerate
In a triangle ABC,ifABC , if\angle A = 30∘30^\circ$$ and $\angle B = 60∘60^\circ , what is the measure of $\angle C$?
Practice More Questions
Official Correct Answer: B. The sum of angles in a triangle is $180^\circ$. So, $\angle C = 180^\circ - \angle A - \angle B = 180^\circ - 30^\circ - 60^\circ = 90^\circ$.
Question 24 of 113
ThinkCAT Practice SetQAGeometry • TrianglesModerate
In triangle XYZ,ifXYZ , if\angle X = 50∘50^\circ$$ and $\angle Y = 70∘70^\circ , what is the measure of $\angle Z$?
Practice More Questions
Official Correct Answer: D. The sum of angles in a triangle is $180^\circ$. So, $\angle Z = 180^\circ - \angle X - \angle Y = 180^\circ - 50^\circ - 70^\circ = 60^\circ$.
Question 25 of 113
ThinkCAT Practice SetQAGeometry • TrianglesModerate
In triangle PQR,ifPQR , if\angle P = 45∘45^\circ$$ and $\angle Q = 75∘75^\circ , find $\angle R$.
TITA Answer:
Practice More Questions
Official Correct Answer: 60. The sum of angles in a triangle is $180^\circ$. So, $\angle R = 180^\circ - \angle P - \angle Q = 180^\circ - 45^\circ - 75^\circ = 60^\circ$.

+ 88 More Official Questions in this Bank

Practice all 113 questions in interactive study mode with instant solution checks, bookmarking, and timer analytics.

Practice All 113 Questions
Free Aspirant Community

Join 2,400+ CAT Aspirants WhatsApp Study Circle

Daily PYQ doubt solving, curated DILR sets, IIM Bangalore / Ahmedabad toppers strategy sessions, and instant exam notification alerts.

Join WhatsApp VIP Group
ThinkCAT Pro Season PassFull Exam Access

Unlock 24 Full-Length CAT CBT Mocks & Percentile Engine

Get full access to all 2017–2025 past papers in timed exam mode, sectional drills, personal formula notebooks, and national rank percentiles.

Upgrade to Pro

Frequently Asked Questions about CAT Triangles Geometry Practice Questions (110+ Questions)

What concepts are covered in the Triangles & Trigonometry Practice Drills practice module?

This module covers Triangles with 113 verified problems ranging from core foundation to high-difficulty CAT exam hall level.

What is the recommended solving time for Triangles & Trigonometry Practice Drills questions?

The ideal target pace is 2.0 to 2.5 mins / question. Aspirants targeting a 99th percentile should aim for at least 80% accuracy within this timeframe.

Where can I find official past year CAT papers for Triangles & Trigonometry Practice Drills?

Official past year exam questions are available in our CAT Triangles Previous Year Questions module.

Related CAT Papers & Topic Mastery Hubs

Explore other slots, sections, and high-weightage topic collections

View Full Archive
Topic Hub

Parent: Geometry Practice Hub

Official PYQ

CAT Triangles Previous Year Questions

121 Qs

Circles & Tangents Practice Drills

96 Qs

3D Solids & Mensuration Practice Drills

79 Qs

Polygons & Angles Practice Drills