如图,四边形ABCD内接于⊙O,BC为⊙O的直径,E为DC边上一点,若AE∥BC,AE=EC=7,AD=6. (1)求AB的长; (2)求EG的长.

问题描述:

如图,四边形ABCD内接于⊙O,BC为⊙O的直径,E为DC边上一点,若AE∥BC,AE=EC=7,AD=6.

(1)求AB的长;
(2)求EG的长.

(1)∵AE∥BC,∴∠EAC=∠ACB,又∵AE=EC,∴∠EAC=∠ECA,∴∠ACB=∠ACE,∴AB=AD=6.(2)如图:延长BA,CD交于P,∵AE∥BC,∴∠EAC=∠ACB,∵AE=EC,∴∠EAC=∠ACE,∴∠ACB=∠ACE,又∵BC是直径,∴∠BAC=90°...