Question

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

Answer 1

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Answer 2

Explanation:

To prove: PQ∣∣ RS

Given: A circle with centre O and diameter AB. Let PQ be the tangent at point A & Rs be the point B.

Proof: Since PQ is a tangent at point A.

OA⊥ PQ(Tangent at any point of circle is perpendicular to the radius through point of contact).

∠OQP=90° …………(1)

OB⊥ RS

∠OBS=90° ……………(2)

From (1) & (2)

∠OAP=∠OBS

i.e., ∠BAP=∠ABS

for lines PQ & RS and transversal AB

∠BAP=∠ABS

i.e., both alternate angles are equal.