Prove that the parallelogram circumscribing a circle is a rhombus.

CBSE Class 10 Maths PYQ · Circles · Quad & Circle · 3 Marks · July 2024 · Standard

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1163 Marks · July 2024 · Standard

Prove that the parallelogram circumscribing a circle is a rhombus.

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Sol.
Here AP = AS, BP = BQ, CR = CQ, DR = DS
$\therefore$ AB + CD = AP + BP + CR + DR
= AS + BQ + CQ + DS
= (AS + DS) + (BQ + CQ)
= AD + BC
$\Rightarrow 2AB = 2 AD$ ($\because$ AB = CD, BC = AD)
$\Rightarrow$ AB = AD
or ABCD is a rhombus.