Thread: Geometric puzzle fun

Code:

          C
 
 
 
 
B           D     E                 A

Triangle ABC has integer sides: perimeter = 96

CD bisects angle ACB ; CE is a median (thus BE = AE).
CD and CE both have integer lengths.

Find the triangle's sides, plus CD and CE.

Hint: CE = 19

can this really be solved without guessing values?

Well, you're given the perimeter=96 :
so "find" a triangle with integer sides and perimeter = 96 : very few!
With sides = a>b>c :
bisector from C = sqrt[ab(1 - k)] where k = c^2 / (a+b)^2

median from C = sqrt[2(a^2 + b^2) - c^2] / 2

And I gave median = 19 as clue...so not too difficult to wrap up.
I'll post/hide the solution (in case I forget!):

Spoiler:

triangle: 13-39-44
bisector = 12