SSC CHSL 2023 PYQ — Question 66

SSC CHSL - 09 March 2023 - Shift 4 • Quantitative Aptitude • Q66

The radii of two concentric circles are x cm and 26 cm. P and S are the points on the larger circle, and Q and R are points on the smaller circle. If PQRS is a straight line and QR = 40 cm and PS = 48 cm, then what is the value of x? (x < 26 cm)

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. 10 $\mathbf{\sqrt5}$ cm.

QR = 40, PS = 48, PO = 26, QO = x

In triangle PTO

PO² = PT² + OT²

⇒ 676 = 576 + OT²

OT = $\sqrt{676 - 576}$ = 10

In triangle QTO

QO² = QT² + OT²

x² = 20² + 10²

x = $\sqrt{500}$ = 10 $\mathbf{\sqrt5}$