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.

Best And Easy Solution Will Be Brainlest..♥️♥️✌️

Answer 1

Hey mate ...
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Soln--->

Let ,

O is the centre of the given circle.

A tangent PR has been drawn touching the circle at point P.

Draw QP ⊥ RP at point P, such that point Q lies on the circle.

∠OPR = 90°  (radius ⊥ tangent)

Also, ∠QPR = 90°  (Given)

∴ ∠OPR = ∠QPR

Now, above case is possible only when centre O lies on the line QP.

Hence, perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

Hope it helps!!

Answer 2

DATA : consider a circle with centre O. Let P be the external point. PA and PB be the 2 tangents.
TO PROVE : PA = PB
CONSTRUCTION : join OP , OA and OB
PROOF : In triangle PAO And triangle PBO,
OA = OA ( COMMON)
angle PAO = angle PBO = 90
OA = OB ( radii )
therefore triangle PAO congruent to triangle PBO ( RHS )
therefore, PA = PB ( CPCT )
HENCE THE PROOF..
HOPE IT HELPS!!♥