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Prove that the parallelogram Cicumscribing a …

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Prove that the parallelogram Cicumscribing a circle is a rhombus

Posted by Rajat Arora 4 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 4 years, 8 months ago

Given: ABCD be a parallelogram circumscribing a circle with centre O.

To prove: ABCD is a rhombus.

We know that the tangents drawn to a circle from an exterior point are equal in length.

Therefore, AP = AS, BP = BQ, CR = CQ and DR = DS.

Adding the above equations,

AP + BP + CR + DR = AS + BQ + CQ + DS

(AP + BP) + (CR + DR) = (AS + DS) + (BQ + CQ)

AB + CD = AD + BC

2AB = 2BC

(Since, ABCD is a parallelogram so AB = DC and AD = BC)

AB = BC

Therefore, AB = BC = DC = AD.

Hence, ABCD is a rhombus.

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