Question

如圖在凹四邊形AOBC中，求證：∠AOB=∠ACB+∠CAO+∠CBO．

Answer 1

證明：連接CO，并延長CO至點(diǎn)D
∵∠AOB=∠AOD+∠BOD，∠AOD=∠ACO+∠CAO，∠BOD=∠BCO+∠CBO
∴∠AOB=∠ACO+∠CAO+∠BCO+∠CBO=（∠CAO+∠CBO）+∠CBO+∠ACB=∠CAO+∠CBO+∠ACB