perplexus.info :: Geometry : Is this circular billiards?

Is this circular billiards? (Posted on 2019-03-18)

Circle O has a radius of 3 units. Points A and B are inside the circle such that AO=1 unit, BO=2 unit, and angle AOB=60 degrees.

CDE is an isosceles triangle inscribed in circle O with CD=DE, point A on CD and point B on DE.

How long are the sides of CDE?

No Solution Yet Submitted by Brian Smith

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Geometer's Sketchpad approximation

| Comment 1 of 4

DE and DC are each 5.92508 and EC is 1.86682 to the accuracy afforded by Geometer's Sketchpad.

Wolfram Alpha lists a possible closed form for the former as 2 pi - 9/(8 pi) ~= 5.9250866852, and for the latter as e^(2/e - 1) pi sin(e pi) ~= 1.866810407 or sqrt(70)/e^(3/2) ~= 1.866840857. An analytic solution would verify or preclude these surmises.

See the diagram:

https://drive.google.com/open?id=134Za8uxQ6DRhii_V3g6fzeh5Ych0KPuG

Posted by Charlie on 2019-03-18 17:09:09

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