Question

Two tangents PA and PB are drawn from an external point P to a circle with centre O. Prove that AOBP is a cyclic quadrilateral.

Answer 1

We are given two tangents PA and PB drawn to a circle with centre O from external point P

We are to prove that quadrilateral AOBP is cyclic

We know that tangent at a point to a circle is perpendicular to the radius through that point.

Therefore from figure

That is

In quadrilateral AOBP,

[Sum of angles of a quadrilateral = 360°]

We know that the sum of opposite angles of cyclic quadrilateral = 180°

Therefore from (1) and (2)

Quadrilateral AOBP is a cyclic quadrilateral.