# Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.

## Answers

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**Step-by-step explanation:**

Draw a circle with center O and take a external point P. PA and PB are the tangents.

As radius of the circle is perpendicular to the tangent.

OA⊥PA

Similarly OB⊥PB

∠OBP=90

∠OAP=90

In Quadrilateral OAPB, sum of all interior angles =360

⇒∠OAP+∠OBP+∠BOA+∠APB=360

⇒90 +90 +∠BOA+∠APB=360

∠BOA+∠APB=180

It proves the angle between the two tangents drawn from an external point to a circle supplementary to the angle subtented by the line segment

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