Homework Help: mathematics

Posted by math... on Monday, June 6, 2011 at 1:46pm.

ABCD is a rectangle, in which BC=2AB. A point E lies on ray CD, such that CE=2BC. Prove that BE perpindicular AC

mathematics - Damon, Monday, June 6, 2011 at 2:20pm
let AB = x
then BC = 2x

then CE = 4x

angle B and angle C are right
AB/BC = BC/CE = 1/2
triangle ABC similar to triangle BCE
Call F intersection of BE and AC
Now angle EBC = FAB (similar triasngles)
Angle FCB = BEC (also same similar triangles)
BUT those angles add to 90 degrees (two angles in right triangle)
so
angle BFC = 90 degrees
mathematics - Anonymous, Monday, June 6, 2011 at 2:23pm
thanks for ur help..

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