Mathematics
Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.
Circles
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Answer
Let PQ be tangent to circle with center O.
We know that,
Tangent at any point of a circle is perpendicular to the radius through the point of contact.
At the point of contact P, RP is perpendicular to the tangent PQ.
We know that,
Radius or diameter will always pass through the centre of the circle.
∴ PR passes through the centre O.
Hence it is proved that perpendicular PR of tangent PQ passes through centre O.
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