Question

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Answer 1

Given :- CD and EF are the tangents at the end points A and B of the diameter AB of a circle with center O .

To prove: CD | | EF

Proof: CD is the tangent to the circle at the Point A

Therefore , ∠ BAD = ${90}^{\circ }$

EF is the tangent to the circle at the point B.

Therefore, ∠ ABE = ${90}^{\circ }$

Thus , ∠ BAD = ∠ ABE (each equal to ${90}^{\circ }$)

But these are alternate interior angles.

therefore, CD | | EF