SSC CGL 2023 PYQ — Question 54

The correct answer is Option 3 i.e.  4$\sqrt{14}$.

PQ touches the smaller circle and OM is perpendicular to QP which divides the PQ into two equal parts.

OM = 13 (radius of smaller circle)

OP = 15 (radius of bigger circle)

In right-angled OMP

⇒ (OP)² = (OM)² + (PM)²

⇒ 15² = 13² + (PM)²

⇒ (PM)² = 225 - 169

⇒ PM² = 56

⇒ PM = √56 = √7 × 2 × 2 × 2 = 2√14

Now,

⇒ PQ = 2 PM

⇒ PQ = 4√14 cm

The length of the chord which touches the smaller circle is 4√14 cm