Question

如图,在△ABC中,AB=5,AC=3,AM平分BAC,CM⊥AM,N为BC中点,求MN的长

Answer 1

延长CM交AB于D,

∵AM⊥CM,∴∠AMC=∠AMD,

∵AM平分∠BAC,∴∠MAC=∠MAD,

∵AM=AM,

∴ΔAMC≌ΔAMD,

∴DM=CM,AD=AC=3,

M为CD中点,

∵N为BC中点,

∴MN=1/2BD=1/2(AB-AD)=1.