Question

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

Answer 1

Suppose CD and AB are two tangents drawn at the ends of diameter QR of a circle with centre O.
We know that the radius and tangent are perperpendular at their point of contact.
∠OQC = ∠ORA = 90^∘
Now, ∠OQC + ∠ORA = 90^∘ + 90^∘ = 180^∘
Since, the sum of cointerior angles on the same side of a transversal line is 180^∘
Hence, CD || AB