Question

In the given figure, PQ and PR are tangents to a circle with centre O and radius 3 cm. If ∠QPR = 60°, then the length of each tangent is:

Options

• `3sqrt3` cm

• 3 cm

• 6 cm

• `sqrt3` cm

Answer 1

`3sqrt3` cm

Explanation:

Given: ∠QPR = 60° 

In △PQO and △PRO

OQ = OR   ...(radii)

PQ = PR   ...(tangents from external point)

OP = OP   ...(common)

△PQO ≅ △PRO   ...(SSS congruence)

∠QPO = ∠RPO

∠QPR = `(60°)/2`

In the right △PQO 

tan(30°) = `(OQ)/(PQ)`

`1/sqrt3 = 3/(PQ)`

PQ = `3sqrt3` cm