What is the length of a segment that is part of an arc that is perpendicular to the diameter ?

Question

Line AB is the diameter of a circle with radius 1 unit and line CD is a chord perpendicular to line AB that cuts line AB at E. If the arc of CAD is 2/3 of the circumferences of the circle, what is the length of segment AE?

Answer 1

AE = 1/2

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Ideas: ∆AED is a 30-60-90 right triangle, and AD = r.

Answer 2

http://i299.photobucket.com/albums/mm286...

AB is perpendicular to CD

OA=OB=OC=OD=r=1

∠COE=∠DOE=60⁰ ==>

∠OCE=30⁰ ==>

OE=0.5*OC=0.5*r=0.5

AE=AO+OE=r+0.5*r=1.5*r=1.5=3/2