Question

prove that the tangents to a circle at the end points of a diameter are parallel

Answer 1

Here AB is a diameter of the circle with centre O, two tangents PQ and RS drawn at points A and B respectively.
Radius will be perpendicular to this tangents

Thus, OA ⊥ RS and OB ⊥ PQ

∠OAR = ∠OAS = ∠OBP = ∠OBQ = 90º

Therefore,

∠OAR = ∠OBQ (alternate interior angles)

∠OAS = ∠OBP (alternate interior angles)

Since alternate interior angles are equal, lines PQ and RS are parallel.
HOPE THIS ANSWER HELP YOU.....
IF THIS HELP PLEASE MARK THIS AS BRAINLEIST.

Answer 2

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⊥ RS8

∠OBS=90

∠OBS=90 o

∠OBS=90 o ……………(2)

∠OBS=90 o ……………(2)From (1) & (2)

∠OBS=90 o ……………(2)From (1) & (2)∠OAP=∠OBS

i.e., ∠BAP=∠ABS

i.e., ∠BAP=∠ABSfor lines PQ & RS and transversal AB

HOPE IT IS HELP FULL TO YOU

PLEASE MATK IT AS BRAINLIST