三角形ABC中角C=90,AB的垂直平分线交BC于M交AB 于N,若AC=8,MB=2MC求AB长
问题描述:
三角形ABC中角C=90,AB的垂直平分线交BC于M交AB 于N,若AC=8,MB=2MC求AB长
答
连接AM
∵MN是AB的垂直平分线,∴△AMN ≌ △BMN,∴MA = MB,∠B = ∠BAM
∵MB = 2MC,∴MA = 2MC,∴∠CAM = 30°,即∠CMA = 60°
∵∠CMA = ∠B + ∠BAM且∠B = ∠BAM,∴∠B = 30°,∴AB = 2AC = 16