Question

In fig., there are two concentric circles with center O and 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 [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Marks

Join OA, OB and OP

In $△OAP$

${PO}^2=O{A}^2+A{P}^2$

${PO}^2=5^2+{12}^2$

${PO}^2=169$

$PO=13$

In $△OBP$

${BP}^2={PO}^2–{BO}^2$

${BP}^2={13}^2–3^2$

${BP}^2=160$

$BP=12.65cm$