△ABC内接于圆O,AB=AC,∠ACB=50,若点P是弧BAC上任一点,则∠BPC的度数;若点P是弧BC上任一点,则∠BPC的度数为.

Question

△ABC内接于圆O,AB=AC,∠ACB=50,若点P是弧BAC上任一点,则∠BPC的度数____;
若点P是弧BC上任一点,则∠BPC的度数为___.

Answer 1

1)∠BPC=∠BAC 而∠ABC=∠ACB 且∠BAC+∠ABC+∠ACB=180 所以∠BPC=∠BAC=80
2)由2中∠BPC与1中∠BPC互补有∠BPC=100