Question

Prove that the radius drawn at the point of contact is perpendicular to the tangent

Answer 1

ans: Let ,

o be the center of circle ,

xy be the tengent at point of

contact p.

to prove : op perpendicular on

xy

construction: q be the point on

xy ,connect Qo

suppose it touches the circle at R .

here , Oq>OR

OQ>OP

same will be the case with all other point on circle .

so, OP is the smallest line that connect xy ,and smallest line is perpendicular.

therefore, OP perpendicular to xy