Geometry and TrigonometryVery hardSegment cut by an angle bisector
Geometry and Trigonometry practice question
In triangle ABC, point D lies on side BC so that AD bisects angle BAC. If AB = 8, AC = 12, and BC = 15, what is the length of BD?
Answer: 6
An angle bisector divides the opposite side in the ratio of the adjacent sides: BD/DC = 8/12 = 2/3. With BD + DC = 15, BD = 6.
Common wrong answers
- If you answered 9
- 9 is DC.
- If you answered 10
- 10 uses the ratio 2/3 on 15 the wrong way.
- If you answered 7.5
- 7.5 halves BC, ignoring the ratio.
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