Question

求证∠BPC=1/2∠A+90°

Answer 1

证明：因为∠A+∠ABC+∠ACB=180°

所以∠ABC+∠ACB=180°-∠A

又因为PB、PC平分∠ABC与∠ACB.

所以∠PBC+∠PCB=1/2(180°-∠A)=90°-2/1∠A

又因为∠BPC+∠PBC+∠PCB=180°

所以∠BPC=180°-（90°-1/2∠A)

即 ∠BPC=1/2∠A+90°