Q. 374.2( 5 Votes )

Prove that the ta

Answer :

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Given: XY is a tangent at point P to the circle.


To prove: OP XY


Construction: Take a point Q on XY other than P and join OQ.


Proof: If point Q lies inside the circle, then XY will become a secant and not a tangent to the circle. So the point Q must lie outside the circle.


OQ > OP


This happens with every point on the line XY except the point P.


So, OP is the shortest of all the distances of the point O to the points of XY.


OP XY


Hence, the tangent at any point of a circle is perpendicular to the radius through the point of contact.

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