Geometry Problem. Post your solution in the comment box below.

Level: Mathematics Education, High School, Honors Geometry, College.

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## Sunday, February 15, 2015

### Geometry Problem 1084: Circle, Chord, Radius, Diameter, Parallel lines, 45 Degrees, Metric Relations

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Join AD, BE, AE.

ReplyDeleteThen 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.