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10. Prove that the angle between the two tangents drawn from an external point to a circleis supplementary to the angle subtended by the line-segment joining the points ofcontact at the centre. |
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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 ⇒90o+90o+∠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 it helps tq./ Step-by-step explanation: |
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