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Find a relation between x and y such that the point (x,y) is equidistant from the points (7.1) and (3.5).
22. In the figure, DE||OQ and DF||OR, show that EF||QR.
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23. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.​

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Maths

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

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

o

…………(1)

OB⊥ RS

∠OBS=90

o

……………(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.