Question

If tangent AB and AC are inclined to each other at an angle of 120 are drawn to a circle with center of radius 6cm. Find the length of each tangent.

Answer 1

let centre of circle be O.
<BAC = 120°

consider ∆ABO and ∆ACO
1) OA =OA --- common side
2) OB = ON --- radii of same circle
3) AB = AC --- tangents from same point
therefore ∆ABO congruent to ∆ACO
therefore <ABO = <ACO = 60°

as tan 60° = √3
therefore in ∆ABO
BO/AB = 6/AB = √3
AB = 6 / √3
AC = 6 / √3

Answer 2

Answer:

2√3cm

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