Q. 374.2( 5 Votes )
Prove that the ta
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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