Problem:
In the adjoining figure, AB is a diameter of the circle, CD is a chord parallel to AB, and AC intersects BD at E, with β AED=Ξ±. The ratio of the area of β³CDE to that of β³ABE is
Answer Choices:
A. cosΞ±
B. sinΞ±
C. cos2Ξ±
D. sin2Ξ±
E. 1βsinΞ±
Solution:
Because ABβ₯DC, arc AD=arcCB and CDE and ABE are similar isosceles triangles. Thus
Area ABE Area CDEβ=(AEDEβ)2
Draw in AD. Since AB is a diameter, β ADB=90β. Thus, considering right triangle ADE,DE=AEcosΞ±, and
(AEDEβ)2=cos2Ξ±
