如图,在△ABCAB=7,AC=11,点M是BC的中点,AD是∠BAC的平分线,MF∥AD,则FC的长为_.
问题描述:
如图,在△ABCAB=7,AC=11,点M是BC的中点,AD是∠BAC的平分线,MF∥AD,则FC的长为______.
答
如图所示,∵AD是∠BAC的平分线,∴
=CD DB
=AC AB
,11 7
∵点M是BC的中点,∴
=CM+DM CM−DM
,解得11 7
=CM DM
.9 2
∵MF∥AD,∴
=CF FA
=CM MD
.9 2
∵CF+FA=11,∴CF=9.