Question

Prove
A tangent to a circle is perpendicular to the radius through the point of contact.

Answer 1

draw a circle draw a tangent XY then draw a op op p should lie on xy
given: a circle with center o and a tangent 
to prove ; op ⊥ XY
construction plot a point q outside the circle but on tangent other than p
proof :xy is a tangent 
p lies on the tangent xy
q lie on xy other than p outside the circle 
∴ op is shorter than oq
is q lies inside the circle then xy will be secant
p is point on the tangent xy
∴ op is the shortest of all other points except point p
∴ op is shorter than oq
∴ op⊥ xy