Please log this mistake into my daughter
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Please log this mistake into my daughter's mistake notebook:
Problem: In triangle ABC, AD bisects angle BAC with D on BC. Given AB=12, AC=8, BC=15, find BD.
Her wrong answer: She wrote AB/BC = BD/DC and solved BD=6.67.
Correct answer: Angle Bisector Theorem gives AB/AC = BD/DC, so BD=9.
Please record this card with tag geometry, cause angle-bisector-ratio, and remind us to review it.
Answer
记下了。
**题面**：三角形 ABC 中，AD 平分 ∠BAC 交 BC 于 D。AB=12，AC=8，BC=15，求 BD。
**错法**：写成 AB/BC = BD/DC，算得 BD≈6.67。
**修法**：角平分线定理是 AB/AC = BD/DC，所以 BD = 12/(12+8) × 15 = 9。
**tag**：geometry · **错因**：angle-bisector-ratio
每天 19:00 复习到期的卡这条已开过了（家里已经到上限 20 条），不需要再加。明天到期的是一张代数消元题（2x+3y=12 与 2x−5y=−4 相减），不在今天这批里——今天到期的卡上面那批里没新加的这张，新卡按 1/3/7/14/30 梯子第一次到期是 2026-09-22。