Question

Prove that the tangent at any point of a circle is perpendicular radius through the point of contact

Answer 1

hope this helps you

Answer 2

Answer:

Step-by-step explanation

Given = a circle with centre O

XY is a tangent with point of contact P

To prove OP Perpendicular to XY

Const = take a point Q on XY other than P and join OQ

proof= Q lies on XY tangent

Q lies outside the circle

( If it lies inside it becomes secant)

OQ is longet than radius OP

OQ>OP

since this happen for every point on the line XY expect point P

OP is the shortest distance of all the distance from point O

i.e OP Perpendicular to XY

( The perpendicular from a point on a line is the shortest)