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Prove that the perpendicular at the poin...

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

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let us assume `_|_` through P passes through `O'`
`O'P _|_ AP` so, `/_ APO' = 90^@`
now, join O & P, if `OP _|_ AP`
then, `/_APO = 90^@`
`/_APO` Should be greater than `/_APO'`
but both the angle are equal
so, `_|_ `from P must passes through O
hence proved
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