Question

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

Answer 1

OB and OC are the two radii of the circle .

AB and AC are the two tangents of the circle.

We know that radius of the circle is perpendicular to the tangent at the point of contact.

∴ OB ⊥ AB and OC ⊥ AC    and ∠ BAC = 40°

∴ IN QUADRILATERAL ABOC ,

∠ BAC + ∠ ACO + ∠ ABO + ∠ BOC = 360° [ angle sum property of a  

                                                                          quadrilateral. ]

⇒ 40° + 90° + 90° + ∠BOC = 360° [ ∵ OB⊥AB and OC ⊥ AC ]

⇒ 220° + ∠BOC = 360°

⇒ ∠BOC = 140°

∴ ∠BOC = 140°

                                                                                                                                                           

Answer 2

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