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.
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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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