(1) Angle ACD= Angle BCE/ Angle ACD+ Angle DCE= Angle BCE+ Angle DCE Angle ACE= Angle DCE.

CA = CD CB = CE/ triangle ACE is equal to triangle D CB.

(2) Triangle ACE is all equal to triangle DCB/ angle CAM= angle PDM.

Angle AMC= Angle DMP and AM are not equal to DM/ Triangle AMC is similar to triangle DMP.

(3) Triangle ACE is all equal to triangle DCB/angle CAP= angle CDP, so ACPD is a four-point circle.

So angle ADC= angle APC is the same: angle BEC= angle BPC.

Isosceles triangle ACD, BCE middle angle ACD= angle BCE/ angle ADC= angle BEC.

So angle APC= angle BPC

The simple questions and big questions in the senior high school entrance examination are not very difficult. The key is to connect before and after. The three small problems are progressive layer by layer.

Using the conclusion of a small problem as a condition often simplifies the problem.

Ask for extra points ask for extra points ask for extra points ask for extra points ask for extra points ask for extra points ask for extra points ask for extra points ask for extra points ask for extra points ask for extra points ask for extra points ask for extra points ask for extra points ask for extra points.