Question

prove that the rangers drawn at the ends of a diameter of a circle are parallel ​

Answer 1

Step-by-step explanation:

REF.Image

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

To prove : CD||EF

Proof : CD is the tangent of the circle at the point A.

∴CD⊥OA

⇒∠OAD=90

∘

⇒∠BAD=90

∘

.......(i)

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

EF⊥OB

⇒∠OBE=90

∘

⇒∠ABE=90

∘

.......(ii)

from (i) and (ii)

∠BAD=∠ABE=90

∘

These are alternate angles

∴CD∣∣EF