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UKMT Senior Kangaroo, 2022

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

A quadrilateral contains an inscribed circle (i.e. a circle tangent to the four sides of the quadrilateral). The ratio of the perimeter of the quadrilateral to that of the circle is $4:3$ . The ratio of the area of the quadrilateral to that of the circle, expressed in its lowest terms, is $a:b$ . What is the value of $100a+49b$ ?

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