Question

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

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

Answer:plz ignore the handwriting.