Answer:
DP = 15.
Step-by-step explanation:
I am assuming that DP EP and FP are peroemdicular bisectors of the sides of ABC.
D is the midpoint of AB so
2x + 14 = 8x - 52
14+52 = 8x - 2x
6x = 66
x = 11.
So side AD = 2(11) + 14 = 36.
Now PC = PA = 39.
So by pythagoras:
DP^2 = AP^2 - AD^2
= 39^2-36^2 = 225
DP = sqrt 225
= 15.
