Maths Olympiad Prep

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Geometry Difficulty 4.7 AIME Find the answer

Ex. 17. A quadrilateral is inscribed in a circle of radius 25, the diagonals of which are perpendicular and equal to 48 and 40. Find the sides of the quadrilateral.

A number or a short expression. Spacing and $ signs are ignored.

Solution

Ex. 17. 510,910,1310,15105 \sqrt{10}, 9 \sqrt{10}, 13 \sqrt{10}, 15 \sqrt{10}. Hint. Find the distances from the center of the circle to the midpoints of the diagonals.

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