Question

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

...Hope this help you....

Answer 2

Explaination :-

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, the 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.