Math, asked by navjeetkaurvirk, 1 year ago

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

Answers

Answered by Anonymous
11
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Hey mate ...
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|| Due to some network issues, I cannot post the pic. ||


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!!.. ya ..☝️

brainlest pls...becoz i need ya...✌️


@amansaini76✅




Answered by THeSentiGuy
4

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!


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