geometry (circle)

Not sure if there is such a reasoning but this is true. Because :
Equal angles at circumference means equal angles at center. For equal angles at center and same radius, the chord will be equal ( congruent triangle SAS).
Converse is also true, because :
Equal chords and equal radius means 2 triangles are congruent (SSS), so angle at center is equal, so is angle at circumference.

2012-08-26 10:00:51 補充：
Suggest you check your textbook see if there is such a reasoning abbreviation, if yes, then write directly. If no, then use the steps above for long question, it does not spend much of your time. For MC question, use the result directly.