The angle of mathematical circle in the first volume of the ninth grade

1.∠ d = ∠ a = 25 (the circumferential angles of the same arc are equal).

∠ ACB = 90 (the circumferential angle of the diameter is a right angle)

∠CBA=90 -25 =65

2. Do OM⊥AB in M, and extend the intersection of OM in N to connect OB.

Then ob = r = 2cm, on = r = 2cm, Mn = om = 1cm (because Mn and om coincide).

According to Pythagorean theorem, BM=√3 cm is obtained.

According to the vertical diameter theorem, AB=2√3 cm is obtained.