Prove that the tangent drawn at the ends of any diameter if a circle are parallel
Jithin12:
Wht to prove
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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
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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Answered by
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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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