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PROVE THAT THE PERPENDICULAR TO THE TANGENT OF A CIRCLE WITH CENTERE O PASSES THROUGH THE CENTERE
Let us consider a circle with center O. Let AB be a tangent which touches the circle at P.
 
We have to prove that the line perpendicular to AB at P passes through the center O. We shall prove this by
contradiction method.

Let us assume that the perpendicular to  AB at P does not pass through the center O.
Let it pass through another point O'. Join OP and O'P.


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