Question

In followinf fig., two concentric circles with centre 0 are of radii 5 cm and 3 cm. from an external point P, tangents PA and PB are drawn to these circles. If AP = 12cm, find BP.

Answer 1

∠ OAP = ∠ OBP = 90°  (radius is .l to tangent at the point of contact)

In right Δ OAP ,

OP² = OA² + AP² 

OP² = 5² + 12² = 25+ 144= 169 

OP = 13 cm

In right Δ OBP,

OP² = OS² + BP² 

BP² = 13² -3² 

BP² =169 - 9 = 160 

BP = `4 sqrt 10` cm