Rectangle ABCD circumscribes the circle of radius 10 cm. Prove that ABCD is a square. Hence, find the perimeter of ABCD.
CBSE Class 10 Maths PYQ · Circles · Quad & Circle · 3 Marks · March 2025 · Standard
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1263 Marks · March 2025 · Standard
Rectangle ABCD circumscribes the circle of radius $10$ cm. Prove that ABCD is a square. Hence, find the perimeter of ABCD.
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For correct figure $AP = AS$ $BP = BQ$ $CR = CQ$ $DR = DS$ Adding the above four equations, $AP + BP + CR + DR = AS + BQ + CQ + DS$ $\Rightarrow AB + CD = AD + CB$ --- (i) Since ABCD is a rectangle $\therefore AB = CD$ and $BC = AD$ $\Rightarrow$ from (i), $2 AB = 2 AD$ or $AB = AD$ Hence ABCD is a square Clearly side of square = diameter of circle = $20$ cm $\therefore$ Perimeter of square = $4 \times 20$ cm = $80$ cm
