【摘 要】
：
经过研究,笔者现已得到:rn定理 如果直角三角形的一个锐角平分线长与对边的比为2 : 3,那么这个锐角为60°.rn已知:如图,在Rt△ABC中,∠C=90°,BD平分∠ABC,且BD: AC =2: 3,求
【机 构】
：
安徽省舒城县杭埠镇中心学校 231323
论文部分内容阅读
经过研究,笔者现已得到:rn定理 如果直角三角形的一个锐角平分线长与对边的比为2 : 3,那么这个锐角为60°.rn已知:如图,在Rt△ABC中,∠C=90°,BD平分∠ABC,且BD: AC =2: 3,求证:∠ABC =60°.rn证明:设 ∠DBC = θ,BD =2a,由BD: AC=2: 3,知AC=3a.在Rt△DBC中,∠C = 90°,所以CD = 2asinθ,BC = 2acosθ,所以AD =(3 - 2sinθ)a.
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