Question

In Fig. there are two concentric circles with centre O of radii 5 cm and 3 cm. from an external point P, tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP.

Answer 1

PA and PB are the tangent drawn from the external

Point P to outer and inner circle repectvely

\(\angle OAP=2 \angle OBP=90^\circ\)

Given OA = 5 cm, OB = 3cm and AP = 12cm

In ΔOAP

OP² = (12cm)² + (5cm)² = 169cm²

In ΔOAP

PB² = OP² - OB²

PB2 = (13cm)² - (3cm)² = 160cm²

PB = \(4\sqrt{10}\)cm

Thus the length of PB = \(4\sqrt{10}\)cm