Solution: ∫D and E are the midpoint of AB and AC sides of equilateral triangle respectively.

∴CD and BE are the heights of AB side and AC side respectively.

∴△BDP and△△△ CEP are right triangles,

And a, d, p, e four-point circle, ∠A=60?

∴∠DPE= 120

∴∠DPB=∠EPC=60

∴∠DBP=30

In the right triangle BDP, DP= 1.

∴BP=2，

Similarly, CP=4 is obtained in CEP of right triangle.

∴BP+CP=6