Geometry - circle properties

I will give you an idea, please complete it by yourself.

Extend AF to meet the circle at H, extend BG to meet the circle at K,
prove that AH and KB are equal chords. Hence, their distance from the centre are equal.

Let the mid-point of CD be M, show that MF = MG by means of the above result. Then, prove that CF = DG. Q.E.D.

Sol
過B作一直線//CD交圓於H
過O作一直線//AH交CD於I, 交BH於J
所以 四邊形BHFG為長方形
O為圓心,AO=OB 且OJ//AH
所以 HJ=BJ
所以 FI=IG
因為 OI垂直CD
所以 CI=ID
所以 CF=CI-FI=ID-IG=GD

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