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Geometry • Circles & Tangents Practice Drills (121 Qs)• Official Answer Keys

CAT Circles Geometry Practice Questions (120+ Questions)

Chords, Tangent-Secant Theorems, Inscribed Angles, Cyclic Quadrilaterals, and Concentric Circles with Diagrams

121 Total Questions
MCQ: 96 (+3 / -1)
TITA: 25 (0 Negative Penalty)
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Core Formulas & Shortcut Matrix: Circles & Tangents Practice Drills

Alternate Segment TheoremFormula #1
\angle TAB = \angle BCA

Angle between tangent AT and chord AB equals angle subtended in alternate segment.

Intersecting Chords TheoremFormula #2
PA × PB = PC × PD

For two chords AB and CD intersecting at internal point P.

Exam Hall Traps & Speedbreakers to Avoid
  • •Forgetting that angle subtended by a diameter at the circumference is always 90 degrees.

Bite-Sized Practice Sets (13 Modules Available)

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Set 01: Circles

Difficulty: Easy
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Set 02: Circles

Difficulty: Hard
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Set 03: Circles

Difficulty: Hard
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Set 04: Circles

Difficulty: Moderate
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Set 05: Circles

Difficulty: Hard
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Set 06: Circles

Difficulty: Hard
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Set 07: Circles

Difficulty: Easy
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Set 08: Circles

Difficulty: Easy
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Set 09: Circles

Difficulty: Easy
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Set 10: Circles

Difficulty: Hard
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Set 11: Circles

Difficulty: Hard
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Set 12: Circles

Difficulty: Easy
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Set 13: Circles

Difficulty: Hard
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Official Exam Questions & Explanations (25 of 121)

Sorted in official convenor sequence
Question 1 of 121
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 2 of 121
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 3 of 121
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 4 of 121
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 5 of 121
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 6 of 121
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 7 of 121
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 8 of 121
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 9 of 121
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 10 of 121
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 11 of 121
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 12 of 121
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.
Question 13 of 121
ThinkCAT Practice SetQAGeometry • CirclesHard
If the radius of a circle is increased by 50%, what is the percentage increase in the area of the circle?
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Official Correct Answer: D. Original area = $\pi r^2$. New radius = 1.5r$. New area = $\pi (1.5r)^2 = 2.25\pi r^2$. Percentage increase = \frac{2.25\pi r^2 - \pi r^2}{\pi r^2} \times 100\% = 125\%$.
Question 14 of 121
ThinkCAT Practice SetQAGeometry • CirclesHard
If the circumference of a circle is increased by $10\% , by what percentage is the area of the circle increased?
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Official Correct Answer: A. Original circumference = 2\pi r$. New circumference = 1.1 \cdot 2\pi r$. New radius = \frac{1.1 \cdot 2\pi r}{2\pi} = 1.1r$. New area = $\pi (1.1r)^2 = 1.21\pi r^2$. Percentage increase = \frac{1.21\pi r^2 - \pi r^2}{\pi r^2} \times 100\% = 21\%$.
Question 15 of 121
ThinkCAT Practice SetQAGeometry • CirclesHard
If the radius of a circle is doubled, by what factor is the perimeter of a square inscribed in the circle increased?
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Official Correct Answer: B. Original radius = r$. New radius = 2r$. Diagonal of the square = 2r$. Side of the square = \frac{2r}{$\sqrt{2}} = r\sqrt{2}$. Original perimeter = 4r\sqrt{2}$. New perimeter = 4(2r\sqrt{2}) = 8r\sqrt{2}$. Factor increase = \frac{8r$\sqrt{2}}{4r$\sqrt{2}} = \sqrt{2}$.
Question 16 of 121
ThinkCAT Practice SetQAGeometry • CirclesHard
If the area of a circle is increased by $400\% , by what percentage is the radius increased?
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Official Correct Answer: B. Original area = $\pi r^2$. New area = 5\pi r^2$. New radius = \sqrt{5}r$. Percentage increase = \frac{$\sqrt{5}$r - r}{r} \times 100\% = 100$\sqrt{5}$\% \approx 223.61\%$. Closest option is 200%.
Question 17 of 121
ThinkCAT Practice SetQAGeometry • CirclesHard
A circle with radius rr is inscribed in a square. If the area of the square is $144 , find the area of the circle.
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Official Correct Answer: A. The side length of the square is $\sqrt{144} = 12$. The radius of the inscribed circle is half the side length of the square, so $r = 6$. The area of the circle is $\pi r^2 = 36\pi$.
Question 18 of 121
ThinkCAT Practice SetQAGeometry • CirclesHard
A circle is inscribed in a right-angled triangle with legs of lengths 6 and 8. Find the radius of the circle.
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Official Correct Answer: B. 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 19 of 121
ThinkCAT Practice SetQAGeometry • CirclesHard
A circle with radius rr is circumscribed around a right-angled triangle with legs of lengths 6 and 8. Find the radius of the circle.
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Official Correct Answer: A. The radius of the circumscribed circle around a right-angled triangle is half the hypotenuse. Here, the hypotenuse is $\sqrt{6^2 + 8^2} = 10$. So, the radius is $\frac{10}{2} = 5$.
Question 20 of 121
ThinkCAT Practice SetQAGeometry • CirclesHard
A circle is inscribed in a right-angled triangle with legs of lengths 5 and 12. Find the radius of the circle.
TITA Answer:
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Official Correct Answer: 2.5. 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 = 5 , b = 12 , and $c = 13$. So, $r = \frac{5 + 12 - 13}{2} = 2.5$.
Question 21 of 121
ThinkCAT Practice SetQAGeometry • CirclesHard
A circle is inscribed in a square of side 10 units. A smaller square is inscribed in the circle such that its sides are parallel to the sides of the larger square. What is the area of the smaller square?
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Official Correct Answer: B. The diameter of the circle is equal to the side length of the larger square, which is 10 units. The diagonal of the smaller square is equal to the diameter of the circle. Let the side length of the smaller square be $s$. The relationship between the side length and the diagonal of a square is given by $s$\sqrt{2} = 10$. Solving for $s$ gives $s = \frac{10}{$\sqrt{2}} = 5\sqrt{2}$. The area of the smaller square is $s^2 = (5\sqrt{2})^2 = 50$ square units.
Question 22 of 121
ThinkCAT Practice SetQAGeometry • CirclesHard
A circle is inscribed in a right-angled triangle with sides of lengths 6, 8, and 10 units. What is the radius of the circle?
Practice More Questions
Official Correct Answer: B. The radius of the inscribed circle in a right-angled triangle can be found using the formula $r = \frac{a + b - c}{2} , where $a$ and $b$ are the legs of the triangle and $c$ is the hypotenuse. Substituting the given values, we get $r = \frac{6 + 8 - 10}{2} = \frac{4}{2} = 2$.
Question 23 of 121
ThinkCAT Practice SetQAGeometry • CirclesHard
A circle with radius rr is inscribed in a square. A smaller square is inscribed in the circle such that its sides are parallel to the sides of the larger square. What is the ratio of the area of the smaller square to the area of the larger square?
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Official Correct Answer: C. The diameter of the circle is equal to the side length of the larger square, which is $2r$. The diagonal of the smaller square is equal to the diameter of the circle, which is $2r$. Let the side length of the smaller square be $s$. The relationship between the side length and the diagonal of a square is given by $s$\sqrt{2} = 2r$. Solving for $s$ gives $s = \frac{2r}{$\sqrt{2}} = r\sqrt{2}$. The area of the smaller square is $s^2 = (r\sqrt{2})^2 = 2r^2$. The area of the larger square is $(2r)^2 = 4r^2$. The ratio of the area of the smaller square to the area of the larger square is $\frac{2r^2}{4r^2} = \frac{1}{2}$. The correct answer is $\frac{1}{2}$.
Question 24 of 121
ThinkCAT Practice SetQAGeometry • CirclesHard
A circle is inscribed in a right-angled triangle with sides of lengths $a , b , and $c(where(wherec$ is the hypotenuse). 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 with sides $a , b , and $c$ is given by $r = \frac{a + b - c}{2}$. This formula is derived from the fact that the area of the triangle can be expressed in two ways: $rs$ (where $s$ is the semi-perimeter) and $\frac{1}{2}ab$. Therefore, $r = \frac{a + b - c}{2}$.
Question 25 of 121
ThinkCAT Practice SetQAGeometry • CirclesHard
A circle is inscribed in a right-angled triangle with sides of lengths $a , b , and $c(where(wherec$ is the hypotenuse). What is the radius of the circle?
Practice More Questions
Official Correct Answer: A. The radius of the inscribed circle in a right-angled triangle with sides $a , b , and $c$ is given by $r = \frac{a + b - c}{2}$. This formula is derived from the fact that the area of the triangle can be expressed in two ways: $rs$ (where $s$ is the semi-perimeter) and $\frac{1}{2}ab$. Therefore, $r = \frac{a + b - c}{2}$.

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Frequently Asked Questions about CAT Circles Geometry Practice Questions (120+ Questions)

What concepts are covered in the Circles & Tangents Practice Drills practice module?

This module covers Circles with 121 verified problems ranging from core foundation to high-difficulty CAT exam hall level.

What is the recommended solving time for Circles & Tangents 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 Circles & Tangents Practice Drills?

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

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