Math, asked by syedibnuana, 1 year ago

Prove that the tangent drawn at the ends of any diameter if a circle are parallel


Jithin12: Wht to prove
yoginr1999p0ocl7: prove tangents are parallel
syedibnuana: Yeh..

Answers

Answered by yoginr1999p0ocl7
3
taking  2 tangents
and diameter as transversal
angle A is 90(given)
    and B is 90(given)
they are || because alternative angles on the same side of transversals are supplementary 

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syedibnuana: Thnk
Answered by hshahi1972
6

Let AB be a diameter of the circle. Two tangents PQ and RS are drawn at points A and B respectively.

Radius drawn to these tangents will be perpendicular to the tangents.

Thus, OA ⊥ RS and OB ⊥ PQ

∠OAR = 90º

∠OAS = 90º

∠OBP = 90º

∠OBQ = 90º

It can be observed that

∠OAR = ∠OBQ (Alternate interior angles)

∠OAS = ∠OBP (Alternate interior angles)

Since alternate interior angles are equal, lines PQ and RS will be parallel

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