Q. 64.8( 5 Votes )

Prove that the pe

Answer :

Let l be a tangent to the circle having centre O. l touches the circle at P. Let m be the perpendicular line to l from P.



We have to prove that m passes through O i.e. O m.


Proof:


If O m, then we can find such M m that O and M are in the same half plane of l.


T l is a distinct point from P.


MPT = 90° and OPT = 90°


M and O are points of the same half plane so this is impossible.


Thus, our assumption is wrong.


O m


The perpendicular drawn to a tangent to the circle at the point of contact of the tangent passes through the centre of the circle.


Hence proved.


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