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UKMT Junior Mathematical Challenge, 2016

Geometry Difficulty 1.0 Junior Find the answer United Kingdom

A cyclic quadrilateral has all four vertices on the circumference of a circle. Brahmagupta (598–670AD) gave the following formula for the area, AA, of a cyclic quadrilateral whose edges have lengths aa, bb, cc, dd: A=(s−a)(s−b)(s−c)(s−d)A = \sqrt{(s-a)(s-b)(s-c)(s-d)}, where ss is half of the perimeter of the quadrilateral. What is the area of the cyclic quadrilateral with sides of length 4 cm, 5 cm, 7 cm and 10 cm?

(A) 6 cm26\text{ cm}^2 (B) 13 cm213\text{ cm}^2 (C) 26 cm226\text{ cm}^2 (D) 30 cm230\text{ cm}^2 (E) 36 cm236\text{ cm}^2

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