Question

From an external point if two tangents are drawn to a circle . prove that they subtended equal angles at the centre

Answer 1



Given
AB and AC are two tangents to a circle from an external point P.

To prove ∠A + ∠BOC = 180° 

Proof
By the theorem, the tangent at any point of a circle is perpendicular to the radius through the point of contact.

Hence ∠OBA = ÐOCA = 90°

In a quadrilateral. ABOC,
∠A + ∠ACO + ∠COB + ∠OBA = 360° (Sum of the angles of a quadrilateral is 360°)


 ∠A + 90° + ∠COB + 90°  = 360° 


∠A + ∠BOC = 180°.