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Geometry Practice Hub (QA) • 551 Qs• Official Answer Keys

CAT Geometry Practice Questions & Drills

Comprehensive Geometry Practice Covering Circles, Triangles, Quadrilaterals, Coordinate Geometry, and 3D Solids with Diagrams

551 Total Questions
MCQ: 447 (+3 / -1)
TITA: 104 (0 Negative Penalty)
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Core Formulas & Shortcut Matrix: Geometry

Apollonius TheoremFormula #1
AB^2 + AC^2 = 2(AD^2 + BD^2)

Where AD is the median to side BC in triangle ABC.

Area of Triangle with InradiusFormula #2
\text{Area} = r × s

Where s = (a+b+c)/2 is the semi-perimeter.

Tangent-Secant TheoremFormula #3
PT^2 = PA × PB

For tangent PT and secant PAB drawn from external point P.

Cyclic Quadrilateral (Ptolemy Theorem)Formula #4
AC × BD = AB × CD + BC × AD

Product of diagonals equals sum of products of opposite sides.

Exam Hall Traps & Speedbreakers to Avoid
  • •Assuming figures are drawn to scale; angles and lengths must be deduced from theorems, not visual appearance.
  • •Confusing inradius (r) with circumradius (R = abc / 4\Delta).
  • •Overlooking that two chords equidistant from the center are equal in length.

Bite-Sized Practice Sets (24 Modules Available)

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Set 01: Triangles

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Official Exam Questions & Explanations (25 of 551)

Sorted in official convenor sequence
Question 1 of 551
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$?
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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 551
ThinkCAT Practice SetQAGeometry • CirclesEasy
A circle has a diameter of 10 cm. What is its radius?
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Official Correct Answer: B. The radius of a circle is half of its diameter. So, if the diameter is 10 cm, the radius is $10 \div 2 = 5$ cm. Hence, the correct answer is B.
Question 3 of 551
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$?
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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 4 of 551
ThinkCAT Practice SetQAGeometry • CirclesModerate
A circle is inscribed in a square with side length 10 cm. What is the area of the circle?
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Official Correct Answer: A. The diameter of the circle is equal to the side length of the square, which is 10 cm. So, the radius is 5 cm. The area of the circle is $\pi r^2 = \pi (5)^2 = 25\pi \text{ cm}^2$. Hence, the correct answer is A.
Question 5 of 551
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?
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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 6 of 551
ThinkCAT Practice SetQAGeometry • CirclesHard
A circle with radius 7 cm is circumscribed around a square. What is the area of the square?
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Official Correct Answer: C. The diagonal of the square is the diameter of the circle, which is $2 \times 7 = 14$ cm. The diagonal of a square with side length $s$ is given by $s\sqrt{2}$. So, $s$\sqrt{2} = 14 , which gives $s = \frac{14}{$\sqrt{2}} = 7\sqrt{2}$. The area of the square is $s^2 = (7\sqrt{2})^2 = 98$ cm$^2$. Hence, the correct answer is C.
Question 7 of 551
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?
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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 8 of 551
ThinkCAT Practice SetQAGeometry • CirclesEasy
If the circumference of a circle is 22π22\pi cm, what is its radius?
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Official Correct Answer: B. The circumference of a circle is given by $2\pi r$. So, $22\pi = 2\pi r$ gives $r = \frac{22\pi}{2\pi} = 11$ cm. Hence, the correct answer is B.
Question 9 of 551
ThinkCAT Practice SetQAGeometry • TrianglesModerate
In △ABC,if\triangle ABC , if\angle A = 30∘30^\circ$$ and $\angle B = 60∘60^\circ , what is $\angle C$?
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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 10 of 551
ThinkCAT Practice SetQAGeometry • CirclesModerate
A circle is inscribed in a right-angled triangle with sides 6 cm, 8 cm, and 10 cm. What is the radius of the circle?
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Official Correct Answer: A. For a right-angled triangle, the radius of the inscribed circle is given by $\frac{a + b - c}{2} , where $a$ and $b$ are the legs and $c$ is the hypotenuse. So, the radius is $\frac{6 + 8 - 10}{2} = 2$ cm. Hence, the correct answer is A.
Question 11 of 551
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?
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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 12 of 551
ThinkCAT Practice SetQAGeometry • CirclesHard
A circle with radius 5 cm is inscribed in a square. What is the area of the square?
TITA Answer:
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Official Correct Answer: 50. The diameter of the circle is equal to the side length of the square, which is $2 \times 5 = 10$ cm. The area of the square is $10^2 = 100$ cm$^2$. Hence, the correct answer is 50.
Question 13 of 551
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:
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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 14 of 551
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?
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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 15 of 551
ThinkCAT Practice SetQAGeometry • TrianglesModerate
In triangle DEF, DE = 6, EF = 8, and DF = 10. What is the area of triangle DEF?
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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 16 of 551
ThinkCAT Practice SetQAGeometry • CirclesEasy
A circle with a radius of 5 units is inscribed in a square. What is the area of the square?
TITA Answer:
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Official Correct Answer: 50. The diameter of the circle is the side of the square, which is 10 units. The area of the square is $10^2 = 100$ square units.
Question 17 of 551
ThinkCAT Practice SetQAGeometry • CirclesModerate
A circle has a radius of 7 units. What is the length of the arc subtended by a central angle of 60 degrees?
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Official Correct Answer: A. The circumference of the circle is $2\pi \times 7 = 14\pi$. The arc length is $14\pi \times $\frac{60}{360} = \frac{7\pi}{3} \approx 7.33$. Hence, the correct answer is A (11.0).
Question 18 of 551
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?
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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 19 of 551
ThinkCAT Practice SetQAGeometry • CirclesHard
A circle is inscribed in a right-angled triangle with legs of lengths 6 and 8 units. What is the radius of the circle?
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Official Correct Answer: A. The radius of the inscribed circle in a right-angled triangle is given by $r = \frac{a + b - c}{2} , where $a$ and $b$ are the legs and $c$ is the hypotenuse. Here, $a = 6 , b = 8 , and $c = 10$. So, $r = \frac{6 + 8 - 10}{2} = 2$.
Question 20 of 551
ThinkCAT Practice SetQAGeometry • TrianglesEasy
If the sides of a triangle are 5, 12, and 13, what is the area of the triangle?
TITA Answer:
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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 21 of 551
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?
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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 22 of 551
ThinkCAT Practice SetQAGeometry • CirclesEasy
If the radius of a circle is 4 units, what is the area of the circle?
TITA Answer:
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Official Correct Answer: 50.27. The area of the circle is $\pi r^2 = \pi \times 4^2 = 16\pi \approx 50.27$ square units.
Question 23 of 551
ThinkCAT Practice SetQAGeometry • CirclesModerate
A circle is inscribed in a square of side 10 units. What is the area of the circle?
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Official Correct Answer: B. The diameter of the circle is the side of the square, which is 10 units. The radius is 5 units. The area of the circle is $\pi \times 5^2 = 25\pi \approx 78.54$ square units.
Question 24 of 551
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?
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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 25 of 551
ThinkCAT Practice SetQAGeometry • CirclesEasy
If the diameter of a circle is 14 units, what is the radius of the circle?
TITA Answer:
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Official Correct Answer: 7. The radius is half of the diameter, so the radius is $\frac{14}{2} = 7$ units.

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Frequently Asked Questions about CAT Geometry Practice Questions & Drills

How many Geometry practice questions are in this collection?

This repository contains 551 curated CAT Geometry practice questions organized by subtopic and difficulty (Easy, Moderate, Hard).

What is the historical weightage of Geometry in the CAT exam?

3 to 5 Questions in QA Section (~15–20% of QA weightage). Excelling in Geometry is critical for securing a 99.0+ percentile.

Are these practice questions accompanied by past year CAT questions?

Yes! You can explore verified official past year questions for this section in our dedicated CAT Geometry Previous Year Questions (2017–2025) archive.

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