smc

Question

Side AB of triangle ABC has length 8 inches. Line DEF is drawn parallel to AB so that D is on segment AC, and E is on segment BC. Line AE extended bisects angle FEC. If DE has length 5 inches, then the length of CE, in inches, is:

Accepted Answer

Draw a line passing through A and parallel to BC. Let FEC = 2n. By alternate-interior-angles or whatever, BAE = n, so BAE is an isosceles triangle, and it follows that BE = 8. ABC DEC. Let CE = x. We have 88+x = 5x 40+5x = 8x x = CE =403. Thus, we choose answer 403.