CAT 2025 Lesson : Circles - Past Questions

11. Past Questions

Question 1

In a triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropped from B, meets the side AC at D. A circle of radius BD (with centre B) is drawn. If the circle cuts AB and BC at P and Q respectively, then AP : QC is equal to
[CAT 2003L]

		1 : 1
		3 : 2
		4 : 1
		3 : 8

Question 2

Two identical circles intersect so that their centres, and the points at which they intersect, form a square of side 1 cm. The area in sq. cm of the portion that is common to the two circles is
[CAT 2005]

		$\dfrac{\pi}{4}$
		$\dfrac{\pi}{2} - 1$
		$\dfrac{\pi}{5}$
		$\sqrt{2} - 1$

Answer: (2)

\dfrac{\pi}{2} - 1

Question 3

ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120 degrees and ∠BAC = 30 degrees, then the value of ∠BCD (in degrees) is
[CAT 2017 S2]

Answer: 90

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