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.

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Solution

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.

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Similar questions

P A

and

P B

are tangents to the circle with centre

O

from an external point

P

, touching the circle at

A

and

B

respectively. Show that the quadrilateral

A O B P

is cyclic.

Q. PQ and PR are two tangents drawn from an external point P to a circle with centre O. Prove that QORP is a cyclic quadrilateral

In the given figure, O is the centre of the circle. PA and PB are tangents. Show that AOBP is a cyclic quadrilateral.

State True or False.

PA and PB are tangents to the circle with centre O from an external point P, touching the circle at A and B respectively. Then the quadrilateral AOBP is cyclic.

Q. Question 2
Two tangents PQ and PR are drawn from an external point to a circle with centre O. Prove that QORP is a cyclic quadrilateral.

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