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Prove that the angle between the two tangents drawn from an external point to a conis supplementary to the angle subtended by the line-segment joining thecontact at the centre.point |
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Answer» Answer: ANSWER 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 o
∠OAP=90 o
In Quadrilateral OAPB, sum of all interior ANGLES =360 o
⇒∠OAP+∠OBP+∠BOA+∠APB=360 o
⇒90 o +90 o +∠BOA+∠APB=360 o
∠BOA+∠APB=180 o
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 Hope this helps you Stay happy and safe Do mark as brainliest ✌️ |
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