Question

prove perpendicular line to radius is a tangent​

Answer 1

Answer:

THEOREM:-  The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Step-by-step explanation:

GIVEN:-  A circle with center O.

               with tangent XY at point of contact P.

TO PROVE:-  OP⊥ XY

PROOF:- Let Q be point on XY

               connect OQ

               suppose it touches the circle at R

Hence,

            OQ is greater than OR

             OQ is greater than OP  [ as OP=OR radius]

Same will be the case with all other points on circle.

Hence, OP is the smallest line that connects XY

and, smallest line is perpendicular

Therefore, OP⊥ XY .                          HENCE PROVED.