2條F.4數學問題 高手幫幫忙!!

1. First, since arc(AM)=arc(BM) (given) ......arc(AM) means arc of AM
thus ∠AOC=∠BOC (eq. arcs, eq. ∠s)

Then clearly OC=OC (common side)
also we have OA=OB (radii of the same circle)

Therefore ΔAOC congruent to ΔBOC.

2a. ∠AOB=∠COD (given)..............(is your question has a typo?)
Also, clear that ∠COB=∠COB (common ∠)
thus ∠AOB-∠COB=∠COD-∠COB
i.e. ∠AOC=∠BOD

2b. Since ∠AOC=∠BOD (proved)
thus arc(AC)=arc(BD) (eq. ∠s, eq. arcs)

2008-12-09 21:39:23 補充：
In the last row of Q1, there is a missing:
Therefore ΔAOC congruent to ΔBOC (SAS).

1)because arcAM=arcBM
so angleMOA=angleMOB(弦比=圓心角比)
AO=BO(半徑)
OC(共邊)

so triangle AOC 相似於 triangle BOC (SAS)

2)如果題目給的資料真係 angle AOB= angle BOD的話,冇得計。
條題目應該係 angle AOB= angle COD

a) because angle AOB=angleCOD
angle AOB= angle AOC+ angle COB
angle COD= angle COB+ angle BOD

so we have ,
angle AOC+ angle COB= angle COB+ angle BOD
then,
angle AOC=angle BOD

b) by a)angle AOC=angle BOD
so, arcAC=arcBD (弦比=圓周角比)