Question

Here Is A Question For You Guys...!!☺️

Prove That The Perpendicular At The Point Of Contact To The Tangent To A Circle Passes Through The Centre.

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Answer 1

$<b>Answer</b>$ Proof

$<b>Step by step explanation</b>$

In the diagram, XY is a tangent through the point P of circle with centre O. OP is the radius.

$\underline{To\: prove:-}$ $\angle{OPY} = \angle{OPX} = 90\degree$

$\underline{Construction:-}$ Q is taken a point on the tangent XY and OQ is joined.

$\underline{To \:proof:-}$ In the diagram OP is the radius of the circle. Since, a tangent touches the circle at a single point therefore any point except P will be longer than OP.
WE KNOW, that from a given point perpendicular is the shortest distance to a given line . Therefore OP is smaller than OQ

$\therefore{OP \: is \: the \: perpendicular \: to \: XY}$

$\angle{OPY} = \angle{OPX} = 90\degree$

Proved