Question

In the following figure, PA and PB are tangents from a point P to a circle with centre O. Then the quadrilateral OAPB must be a ______ 

Options

• Square

• Rhombus

• Cyclic quadrilateral

• Parallelogram

Answer 1

In the following figure, PA and PB are tangents from a point P to a circle with centre O. Then the quadrilateral OAPB must be a Cyclic quadrilateral.

Explanation: 

Since tangent and radius intersect at a right angle,

So,

∠OAP = ∠OBP = 90°

⇒ ∠OAP + ∠OBP = 90° + 90° = 180°

Which are opposite angles of quadrilateral OAPB.

So the sum of the remaining two angles is also 180°.

Therefore Quad OAPB is cyclic Quadrilateral.