2026 · Q67
ABC is a triangle such that ∠ABC = 120°. If BD is the bisector of ∠B that meets AC at D, then what is the ratio of the area of ΔABD to the area of ΔCBD?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AAB : BC
- BBC : AB
- CAB² : BC²
- D1 : 1
Explanation
Triangles ABD and CBD share the altitude from B to the line AC, so their areas are in the ratio AD : DC of their bases. By the angle-bisector theorem, AD/DC = AB/BC. Therefore area(ABD) : area(CBD) = AB : BC, option A.