2025 · Q14
In a triangle ABC, AB = 2 cm, BC = 4 cm and AC = 3 cm. The bisector of angle A meets BC at D and the bisector of angle B meets AD at E. What is AE : ED equal to?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A5 : 4
- B5 : 3
- C4 : 3
- D3 : 2
Explanation
By the angle-bisector theorem, BD/DC = AB/AC = 2/3, so with BC = 4, BD = (2/5) × 4 = 8/5. In ΔABD, BE bisects angle B, so AE/ED = AB/BD = 2/(8/5) = 10/8 = 5/4, option (a).