Question

O is the center of a circle and p is the external point of the circle. Now pq and pr is the two tangent of this circle. Now op is 13cm so what is the value of pq?

Answer 1

Solution -
O is the centre of circle ,

P is an external point , PQ and PR are tangent drawn from point P .

Draw radii OQ , OR i.e ,
OQ perpendicular to tangent QR ...............tangent theorem

also , OR perpendicular to tangent PR ......tangent theorem

therefore , In ∆POR angle PRO is 90°,

By converce of 30°,60°,90° theorem

hypo OP is 13 cm i.e OP = 13 cm
therefore , PR is side opp. to 30° = 1/2 ×Op,
OP = 1/2 × 13
= 6.5 cm.

Thanks