Prove that the parallelogram circumscribing a circle is a rhombus.
CBSE Class 10 Maths PYQ · Circles · Quad & Circle · 3 Marks · March 2025 · Standard
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1243 Marks · March 2025 · Standard
Prove that the parallelogram circumscribing a circle is a rhombus.
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Correct figure We know that lengths of tangents drawn from an external point to a circle are equal $\therefore AP = AS$ --- (1) $BP = BQ$ --- (2) $CR = CQ$ --- (3) $DR = DS$ --- (4) Adding (1), (2), (3) and (4), we have $(AP + BP) + (CR + DR) = AS + (BQ + CQ) + DS$ $\Rightarrow AB + CD = BC + AD$ $\therefore AB = CD$ and $BC = AD$ $\therefore AB = BC = CD = AD$ Therefore, ABCD is a rhombus.
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