Problem:
Triangle in the figure has area . Points and , all distinct from , and , are on sides and respectively, and . If triangle and quadrilateral have equal areas, then that area is
Answer Choices:
A.
B.
C.
D.
E. not uniquely determined
Solution:
Draw in line . Since Area Area Area , and Area Area Area , it follows that Area Area , Since these two triangles have a common base , the altitudes on this base must be equal. That is, and are equidistant from line , so . Then, using similar triangles and ,
.
Thus Area Area .
