Question
Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.
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Text solutionVerified
Given a circle with center and the tangent intersecting circle at point
and prove that
We know that tangent of the circle is perpendicular to radius at points of contact Hence
So,
Now lets assume some point
Such that
Hence
From eq &
Which is possible only if line passes though
Hence perpendicular to tangent passes though centre
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Question Text | Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle. |
Answer Type | Text solution:1 |
Upvotes | 150 |