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Prove that the range ts drawn …

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Prove that the range ts drawn at the ends of a diameter of a circle are parallel

Posted by Ryan George 5 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years ago

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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Posted by Kanika . 4 days, 12 hours ago

CBSE > Class 10 > Mathematics