SOLUTION: In the diagram below, ΔABC is circumscribed about circle O and the sides of ΔABC are tangent to the circle at points D, E, and F. http://imageshack.us/photo/my-images/8

Algebra ->  Circles -> SOLUTION: In the diagram below, ΔABC is circumscribed about circle O and the sides of ΔABC are tangent to the circle at points D, E, and F. http://imageshack.us/photo/my-images/8      Log On


   

Question 737531: In the diagram below, ΔABC is circumscribed about circle O and the sides of ΔABC are tangent to the circle at points D, E, and F.
http://imageshack.us/photo/my-images/849/geou.png/
If AB=20, AE=12, and CF=15, what is the length of AC?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

If AB=20,
AE=12, and
CF=15,
what is the length of AC?
Incenter :
The location of the center of the incircle. The point where the angle bisectors meet.

If AB=20 and AE=12, then EB=8
since EO=FO=DO, angle EBO= angle FBO, and BO=BO.....=> triangles EOB and OBF are congruent, then EB=BF=8

since EO=FO=DO, angle EAO= angle DAO, and AO=AO.....=> triangles EAO and DAO are congruent, then AE=AD=12
since EO=FO=DO, angle DCO= angle FCO, and AO=AO.....=> triangles DCO and FCO are congruent, then DC=CF=15
since the length of AC=AD%2BDC, then AC=12%2B15=27