Question

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

Answer 1

Step-by-step 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.

So, lines are parallel.

therefore PQ||RS.

Answer 2

Answer:

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