CAT 2025 Lesson : Class Discussion: Geometry - Circles 17 to 24

Class Discussion - Circles

Question 17

In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is
[CAT 2018 S1]

		$\sqrt{14}$
		$\sqrt{11}$
		$\sqrt{13}$
		$\sqrt{12}$

Question 18

A chord of length 5 cm subtends an angle of

60 \degree

at the centre of a circle. The length, in cm, of a chord that subtends an angle of

120 \degree

at the centre of the same circle is
[CAT 2018 S2]

		$2 \pi$
		8
		$6\sqrt2$
		$5\sqrt3$

Question 19

In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, is
[CAT 2019 S1]

		0.5
		1.5
		2.5
		3.5

Question 20

AB is a diameter of a circle of radius 5 cm. Let P and Q be two points on the circle so that the length of PB is 6 cm, and the length of AP is twice that of AQ. Then the length, in cm, of QB is nearest to
[CAT 2019 S1]

		7.8
		8.5
		9.1
		9.3

Question 21

Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, is
[CAT 2019 S2]

		$\dfrac{\pi}{3}$
		1
		$\sqrt2$
		$\dfrac{1}{\sqrt2}$

Question 22

On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two-thirds of the painted area then the perimeter of the rectangle in inches is
[CAT 2020 S1]

		$3 \sqrt\pi \left(5 + \dfrac{12}{\pi}\right)$
		$4 \sqrt\pi \left(3 + \dfrac{9}{\pi}\right)$
		$3 \sqrt\pi \left(\dfrac{5}{2} + \dfrac{6}{\pi}\right)$
		$5 \sqrt\pi \left(3 + \dfrac{9}{\pi}\right)$

Question 23

Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the length of PQ, in meters, is nearest to
[CAT 2020 S2]

		6.6
		7.2
		7.8
		8.8

Question 24

Let C1 and C2 be concentric circles such that the diameter of C1 is 2 cm longer than that of C2. If a chord of C1 has length 6 cm and is a tangent to C2, then the diameter, in cm, of C1 is

[CAT 2020 S2]

Answer: 10

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