1)

Connecting CE and AE

Because arc AC= arc CE

So AC = ce

Because cm = AC

So AC = ce = cm

So a, m and e are on a circle with c as the center and AC as the radius.

So the circumferential angle ∠ AEM = the central angle ∠ACM/2.

Because AB is the diameter

So ∠ACB and ∠AEB are right angles, that is ∠ ACM = 90 degrees.

So ∠ AEM = 45 degrees, which means ∠ AEN = 45 degrees.

Because AEB = 90 degrees.

So ∠ Ben = ∠ AEN = 45 degrees.

So arc AN= arc BN

2)

Let AE and BC give it to H.

Because be = 6 and AB = 10.

So according to Pythagorean theorem AE = 8.

Because arc AC= arc CE

So ∠ ABC = ∠ EBC

So eh/ah = be/ab = 3/5.

So eh = 3

Judging from the above questions, ∠ aen = ∠ Ben

So EM divided ∠BEH equally.

So hm/BM = eh/be = 3/6 = 1/2.

So s △ Ben = (s △ beh) * (2/3)

=(BE*EH/2)*(2/3)

=(6*3/2)*(2/3)

=6

For reference! JSWYC