CAT 2025 Slot 1 QA Question 18: In a circle with center C and radius $6\sqrt{2}$ cm, PQ and SR are two parallel chords separated by one of the diameters. If $\angle PQC = 45^\circ$, and the ratio of the perpendicular distance of PQ

Question

In a circle with center C and radius $6\sqrt{2}$ cm, PQ and SR are two parallel chords separated by one of the diameters. If $\angle PQC = 45^\circ$, and the ratio of the perpendicular distance of PQ

Accepted Answer

Let M and N be the feet of the perpendiculars from C to chords PQ and SR respectively.
In triangle CPQ, CP = CQ = radius = $6\sqrt{2}$. Since $\angle PQC = 45^\circ$, triangle CPQ is an isosceles right triangle.
$CM = CQ\cos 45^\circ$
$CM = 6 \sqrt{2} 	imes \dfrac{1}{\sqrt{2}} = 6$

The perpendicul