Question

In the given figure, PA and PB are the tangent segments to a circle with centre O. Show that the points A, O, B and P are concyclic.

Answer 1

Here, OA = OB
And OA ⊥ AP,OA ⊥ BP (Since tangents drawn from an external point are perpendicular to the radius at the point of contact)
∴ ∠ OAP = 90°  , ∠ OBP = 90°
∴ ∠OAP +∠ OBP = 90° +  90° = 180°
∴ ∠ AOB + ∠APB =180°  (Since, ∠OAP +∠OBP +∠AOB  +∠APB = 360° )
Sum of opposite angle of a quadrilateral is 180° .
Hence A, O, B and P are concyclic.