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People's Education Press ninth grade mathematics exercise 24. 1 the first 1 1 and 12 (about the verification of polygons inscribed in a circle)
Question 1: aoc=cob is obtained from arc AC= arc BC.

Aob= 120。

So aoc=60

Ao = co in triangular aoc

So oac=60

Aob= 120。

So ac//ob

Similarly, oa//bc and oacb are parallelograms.

oa=ob

So oacb is a diamond.

Question 2: apc=bpc, ac=bc.

The triangle acb is isosceles.

Apb= 120。

So acb=60

So acb is equilateral.