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. 23​
B. 35​
C. 23​​
D. 3​
E. 22+3​​
Solution:
In the figure, ∠AEB=90∘ since AB is a diameter. Thus AE is an altitude of equilateral △ABC. It follows that △ABE is a 30∘−60∘−90∘ triangle and AE=AB23​​=3​.
