Problem:
Let β³ABC be an isosceles triangle with BC=AC and β ACB=40β Construct the circle with diameter BC, and let D and E be the other intersection points of the circle with the sides AC and AB, respectively. Let F be the intersection of the diagonals of the quadrilateral BCDE. What is the degree measure of β BFC?
Answer Choices:
A. 90
B. 100
C. 105
D. 110
E. 120
Solution:
Because BC=AC and β ACB=40β, it follows that β BAC=β ABC=70β. Because β BAC=21β(BCβDE) and BC=180β, it follows that DE=40β. Then
Because D and E lie on the circle with diameter BC, both β BDC and β BEC are right angles, so β ADF and β AEF are also right angles. Therefore in quadrilateral AEFD