Question

I will mark you brainliest. Please help.

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

Answer 1

Answer:

Using Contradiction Method

Step-by-step explanation:

Consider a circle with centre O. suppose perpendicular drawn on AP at P(AP is a tangent from an external point A.) doesn't passes through the centre, it passes through some other point O'. Join OP.

∴, ∠O'PA = 90°

   ∠OPA = 90°    (radius is ⊥ to tangent at the point of contact.)

⇒∠O'PA = ∠OPA

this is possible iff O and O' coincide.

This contradicts our assumption that the ⊥ on AP at P doesn't passes through the centre