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题目(2007年全国初中数学竞赛(山东赛区)预赛题第14题)如图1,在Rt△ABC中,∠C=90°,BC =2AC,AD是∠BAC的平分线.求证:AB+2BD=5AC.
Title (Question 14 of the 2007 National Junior High School Mathematics Competition (Shandong Division) Preliminaries) Figure 1. In Rt △ ABC, ∠C=90°, BC =2AC, AD is the bisecting line of ∠ BAC. Proof: AB+ 2BD=5AC.