Can two of the angle bisectors of a triangle intersect perpendicularly? Why?

I thought yes, because I think it works with an isosceles triangle.

Question

Can two of the angle bisectors of a triangle intersect perpendicularly? Why? 

I thought yes, because I think it works with an isosceles triangle.

phi · Answer

Draw two angles, with their angle bisectors meeting at 90º angle
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phi · Answer

I claim angle a+angle b= 90

a is 1/2 the upper angle,  so the upper angle is 2a
same for b,  it's 1/2 the other angle in the triangle, which must be 2b
2a+2b= 180,  and we have not added in the 3rd angle.  So it looks like angle bisectors can never be perpendicular.