In triangle ABC, AB=AC, BC=1, and

Question

In triangle ABC, AB=AC, BC=1, and <BAC=36 degrees. Let D be the point on side AC such that <ABD=<CBD. Find AB.

jdoe0001 · Answer

got any pictures  you'd like to share with us?

anonymous · Answer

Sure just a sec

anonymous · Answer

|dw:1382293478791:dw|

jdoe0001 · Answer

|dw:1382295576274:dw|

due to the Angle Bisector Theorem, we thus have 2 SIMILAR triangles, and their side will correspond

anonymous · Answer

Ah, so AB=1. Thanks a lot!!

jdoe0001 · Answer

hmmm, ... no... I misread you I gather, AB cannot be equal to BC...

jdoe0001 · Answer

lemme redo that ... shoot..

jdoe0001 · Answer

I misread AB = BC... is just AB = AC... so |dw:1382296170168:dw|

anonymous · Answer

Which means the base angles are each 72. And since BD is the angle bisector, <ABD=<CBD=36=<BAD. This means that <ADB=72. Triangles BAD and BDC are congruent by AAS, so <ABD=<DBC, <ADB=<BCD and BD is shared. So, this is an equilateral triangle and AB=1. I think I have this one figured out, thanks!

jdoe0001 · Answer

yw