Q23 of 40 Page 1

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

To Prove: CD || EF



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


⇒ CD⟘ OA


⇒ ∠ OAD = 90° and ∠ BAD = 90° ... (1)


EF is the tangent to the circle at point B.


⇒ EF ⟘ OB


⇒ ∠ OBE = 90° and ∠ ABE = 90° … (2)


From (1) and (2),


∠ BAD = ∠ ABE = 90°


These are alternate angles.


Therefore, CD || EF


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