1。 It is proved that the sum of these two angles is equal to 180 degrees, so we can know that ADBC is a four-point circle.

Then angle BDC= angle BAC=60 degrees, angle ADC= angle ABC=60 degrees.

Angle ABC= Angle BAC=60 degrees (known)

Therefore, angle ADC= angle BDC, that is, DC bisecting angle ADB.

2。 Under the condition of 1, we know that ABC is a regular triangle, then we know that CF=BE from AF=CE, and then we prove that the triangle ABE and BCF are congruent.

So Angel ·FBC = Angel Pei. . . DH=2, HC=2, root number 3, then CD=2+2, root number 3.