Question

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

Answer 1

Step-by-step explanation:

Given ,

we are given a circle with center "O" and a tangent AB to the circle at a point p.

to prove - OP perpendicular AB.

const- take a point Q on the tangent AB other than the point of contact P. join OQ.

proof- we know that the point Q is a point lies outside the circle.

let OQ intersect the circle at R.

then OR smaller than OQ .(1)

OP equals to OR ( radius of circle )-(2)

OP is smaller than OQ . (from eqn 1 and 2 )

OP is shorter than any other line segment joining O to any point of AB other than P.

But shorter distance between a point and a line is the perpendicular distance.

Hence , OP perpendicular AN.