Problem:
Segment AB is both a diameter of a circle of radius 1 and a side of an equilateral triangle ABC. The circle also intersects AC and BC at points D and E, respectively. The length of AE is
Answer Choices:
A. 23β
B. 35β
C. 23ββ
D. 3β
E. 22+3ββ
Solution:
In the figure, β AEB=90β since AB is a diameter. Thus AE is an altitude of equilateral β³ABC. It follows that β³ABE is a 30ββ60ββ90β triangle and AE=AB23ββ=3β.