Question

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EAF+角BCD）

要有过程！！

Answer 1

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∠E   ①

     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）