Question

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

Answer 1

Answer:

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Step-by-step explanation:Given : CD and EF are tangents at the endpoints

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.

ZBAD = 90

[Radius is _ to the tangent at the point of contact]

EF is the tangent to the circle at point B.

B

ZABE = 90 [Radius is ] to tangent at point of contact]

ZBAD = ZABE (each equal to 90)

Thus

But these are alternate interior angles.

CD || EF