Question

From an external point A two tangents AB & AC are drawn to a circle with centre O such that angle BOC=100°.
Find:-
i) angle BAC.
ii) angle OAC​

Answer 1

Given :  an external point A two tangents AB & AC are drawn to a circle with centre O such that angle BOC=100°.

To Find : i) angle BAC

ii) angle OAC

Solution:

AB & AC are tangents

=> ∠OBA = ∠OCA = 90°

∠BOC=100°.

∠OBA + ∠OCA + ∠BOC + ∠BAC = 360°   ( sum of angles of a Quadrilateral )

=> 90° +  90° + 100°.  + ∠BAC = 360°  

=> ∠BAC =  80°

OC bisect ∠BAC

=> ∠OAC =  80°/ 2

=> ∠OAC =  40°

∠BAC =  80°

∠OAC =  40°

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