1, connecting OA, and the easy-to-prove angle MAO=30 degrees;

2. It is easy to know that triangle CMN and triangle OMN are equilateral triangles-angle AMO=60 degrees-angle MOA=90 degrees;

3.om = 1/2am from (1) (2); And CN=MN=OM, so AM=CN+MN.

The third question:

1, connect OA and oc, intercept CM 1=AM on CB, and connect om1;

2. It is easy to know that OC=OA, angle OAM= angle OCM 1=30 degrees, CM 1 = AM- triangle OMA are all equal to triangle OM 1C-OM = OM 1, and angle MOA= angle M65438.

3. Easy-to-know angle AOC= 120 degrees, angle MOA= angle m 1oc- angle MOM 1= 120 degrees; From angle MON=60 degrees-angle M 1ON=60 degrees-angle MON= angle m1on;

4, by (2)OM=OM 1, (3) anglemon = anglemen1on, no = no- triangle OMN is equal to triangle om1n.

-MN = m 1N；

5, by (1)CM 1=AM, (4) Mn = m1n = cm1+NC-Mn = am+NC.

The proof about the center O has been appropriately omitted (angle, etc.). ) so it should be clear. I wish you good grades!