Question

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

Answer 1

Let O be the centre of the given circle. AB is the tangent drawn touching the circle at A. Draw AC ⊥ AB at point A, such that point C lies on the given circle. ∠OAB = 90° (Radius of the circle is perpendicular to the tangent) Given ∠CAB  = 90°   ∴ ∠OAB = ∠CAB This is possible only when centre O lies on the line AC. Hence, perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

Answer 2

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