Prove that the tangent at any point of a circle is perpendicular to thr radius through the point of contact.
Asked by anusarika mohanty | 21st Dec, 2013, 07:21: PM
Given: A circle C (O, r) and a tangent AB at a point P.
To Prove: OP is perpendicular to AB.
Construction: Take any point Q, other than P, on the tangent AB. Join OQ.
Since, Q is a point on the tangent AB, other than the point of contact P, so Q will be outside the circle.
Let OQ intersect the circle at R.
But, among all the line segments, joining the point O to a point on AB, the shortest one is the perpendicular from O on AB.
Hence, OP is perpendicular to AB.
Answered by | 21st Dec, 2013, 09:27: PM
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