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Geometry Problem. Post your solution in the comment box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the diagram below to enlarge it.
Join AD, BE, AE. Then ACDB and BCDE are isosceles trapeziums. Since ∠CBE = ∠BCD = 45°, thus ∠ABE = 90°. i.e. AE is diameter and AE=2r. Now since BE=CD=c, so in ΔABE, a²+c²=4r². Also since AD=BC=b, so in ΔADE, b²+d²=4r².