Question

prove that the perpendicular at the point of contact to the tangent to the circle passes through the centre
plzzz answer...​

Answer 1

Answer:

Given : let us assume a circle with centre O

and AB a tangent which intersecting circle at point P

To prove : OP perpendicular AB

Proof :

Tangent of circle is a perpendicular to radius at point of contact

hence, OP perpendicular AB

so, angle OPB = 90 ° . ........ (1)

let us assume some point X

such that, XP perpendicular AB

hence, angle XPB = 90° . ...... (2)

from 1 and 2

angle OPB = angle XPB = 90°

which is possible only if line XP passes through O

hence, perpendicular to tangent passes through centre