Question

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

Answer 1

At the point of contact, the radius of the circle is also perpendicular to the tangent. This makes the radius and the perpendicular at the  least parallel. The fact that they both intersect at the point of contact makes them coincident. Since they are coincident and the radius originated at the center, the perpendicular must also go through the center.

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