In the given figure, AB and AC are tangents to the circle with center O such that ∠BAC = 40°. Then, ∠BOC is equal to

Question

In the given figure, AB and AC are tangents to the circle with center O such that ∠ BAC = 40°. Then, ∠ BOC is equal to

Philoid · Accepted Answer

As AB and AC are tangents to given circle,

We have,

OB ⏊ AB and OC ⏊ AC

[∵ Tangents drawn at a point on circle is perpendicular to the radius through point of contact]

So, ∠OBA = ∠OCA = 90°

In quadrilateral AOBC, By angle sum property of quadrilateral, we have,

∠OBA + ∠OCA + ∠BOC + ∠BAC = 360°

90° + 90° + ∠BOC + 40° = 360°

∠BOC = 140°