Question

Prove that tangents drawn at the end of diameter is parallel

Answer 1

Prove that tangents drawn at the end of diameter is parallel

Answer 2

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✭ Tangents drawn at the end of a diameter are parallel

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Given that AB is a diameter we can use the theorem

➝ Tangents ⊥ radius

➝ OA ⊥ PQ

And hence ,

»» ∠OAP = 90° -eq(1)

Also,

»» OB ⊥ MN

And so,

➳ ∠OBN = 90° -eq(2)

❍ By eq(1) and eq(2)

➳ ∠OAP = ∠OBN = 90°

With the help of converse of Alternate interior angles theorem we can finalise that,

≫ $\sf\orange{PQ || MN }$

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