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The ninth grade math problem book 1 ~ urgent ~ ~
(1) Angle ACB=90 degrees AB is the diameter.

(2) AC parallel ODOD⊥BC, vertical foot e, angle OEB=90 degrees, AC parallel OD.

(3)CE=BEO is the center of the circle, OD⊥BC. According to the vertical diameter theorem, we can get the bisection BC of point E, and we can also get the arc length of arc CD and arc BD.

(4) Triangle ABC and Triangle OBE are similar triangle angles ACB= angle OEB=90 degrees, and angle ABC= angle OBE.

(5) △ oce △ obeoe = OE, angle OEC= angle OEB, EC=EB.