延长四边形ABCD的对边AD,BC交于F;DC,AB交于E,若角AED,角AFB平分线交于O,求证:角EOF=1/2（角

证明：连接OA
∵角AED,角AFB平分线交于O
∴ ∠EOF=∠OAB+1/2∠F+∠OAD+1/2∠E
=∠EAF+1/2∠F+1/2∠E①
又 ∠BCD=∠F+∠CDF
=∠F+∠EAF+∠E ②
由①②得 ∠EOF=∠EAF+1/2∠F+1/2∠E
=1/2∠EAF+1/2∠EAF+1/2∠F+1/2∠E
=1/2∠EAF+1/2∠BCD
=1/2(∠EAF+∠BCD)
∴角EOF=1/2（角EAF+角BCD）