Question

Prove that the tangents drawn at ends of a diameter
of a circle are equal
​

Answer 1

Answer:

Given :

CD and EF are the tangents at the ned points A and B of the diameter AB of a circle with centre O.

To prove :CD∥EF.

Proof :

CD is the tangent to the circle at the point A.

Therefore, ∠BAD=90°

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

Therefore, ∠ABE=90 °

Thus, ∠BAD=∠ABE=90°

But, these are alternate interior angles.

Therefore, CD∥EF.