Triangle ABC with BC=10, AC=11 and AB = 12.

Point P is inside triangle ABC, such that triangles APB, APC and BPC have equal areas.

What are lengths od AP, BP abd CP?

Work so far:

area of ABC = 33SQRT(39) / 4

triangle APB : height from P = (33SQRT(39)/2) / 36

triangle APC : height from P = (33SQRT(39)/2) / 33

triangle BPC : height from P = (33SQRT(39)/2) / 30

From that, how would you calculate lengths of AP, BP and CP?

I keep going around in circles! Thanks.