CDS 2025 · PYQ · Triangles / Angle Bisector · easy
In a triangle ABC, the bisector of angle A cuts BC at D. If AB + AC = 10 cm and BD : DC = 3 : 1, then what is the length of AC?
- A.2·5 cm✓ Correct
- B.6 cm
- C.7·5 cm
- D.8 cm
By the angle bisector theorem, BD/DC = AB/AC = 3/1. So AB = 3·AC. Given AB + AC = 10, so 3·AC + AC = 10, giving 4·AC = 10, hence AC = 2.5 cm.
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