2025 · Q15
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?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A2.5 cm
- B6 cm
- C7.5 cm
- D8 cm
Explanation
By the angle-bisector theorem, BD/DC = AB/AC = 3/1. With AB + AC = 10, write AB = 3k, AC = k; then 4k = 10 gives k = 2.5, so AC = 2.5 cm, option (a).