Two concentric circles have radii of 13 cm and 15 cm, respectively. A chord AB of the larger circle intersects the smaller circle at points P and Q. If PQ = 10 cm, then AB will be:

Q.Two concentric circles have radii of 13 cm and 15 cm, respectively. A chord AB of the larger circle intersects the smaller circle at points P and Q. If PQ = 10 cm, then AB will be: (a) 28 cm (b) 20 cm (c) 18 cm (d) 16 cm

Answer: C

A perpendicular OX is drawn from point O to AB.

From ∆OPX, we get:
\(OX^2 = OP^2 - PX^2 = 13^2 - (\frac{10}{2})^2\)
\( = 169 - 25 = 144\)
∴ \(OX = \sqrt{144} = 12\)

From ∆OXB, we get:
\(XB^2 = OB^2 - OX^2 = 15^2 - 12^2\)
\( = 225 - 144 = 81\)
∴ \(XB = \sqrt{81} = 9\)

Therefore, \(AB = 2 × XB = 2 × 9 = 18\) cm.