三角形ABC中,角A=36度,AB=AC,BD是∠ABC的平分线,设CD=a,AD=b,AB=c,求证b²=a

学习时间:2026-04-01 08:59:04 阅读：4591

三角形ABC中,角A=36度,AB=AC,BD是∠ABC的平分线,设CD=a,AD=b,AB=c,求证b²=ac

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2026-04-01 08:59:04

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∵∠A=36° AB=AC∴∠ABC=∠C=(180°-36°)÷2=72°又BD平分∠ABC∴∠CBD=72°÷2=36° ∠ABD=36°=∠BAD∴△BCD∽△ABC 且BC=BD=AD=b∴AB:BC=BC:CD∴b²=ac