Question

if two tangents are inclined at an angle of 60 degree of a circle with radius 6 cm and the length of each tangent is​

Answer 1

${\mathfrak{\pink{\underline{\underline{Answer:-}}}}}$

The length of each tangent is​ 13√3 cm.

${\mathfrak{\pink{\underline{\underline{Explanation:-}}}}}$

Let PA and PB be two tangents to a circle O and radius 13 cm.

We are given ∠APB = 60°

We know that two tangents drawn to a circle from an external point are equally inclined to the segment joining the center to the point.

∴ ∠APO = ∠BPO = 1/2 × ∠APB = 1/2 × 60° = 30°

Also, OA ⊥ AP and OB ⊥ BP  (radius ⊥ tangent at point of contact)

In right ΔOAP,

tan 30° = 13/PA

⇒ 1/√3 = 13/PA

⇒ PA = 13√3 cm.

∴ PA = PB = 13√3 cm.  (Length of tangents drawn from an external point to the circle are equal).