2024 · Q27
In a triangle ABC, D is a point on BC. If AB.DC = AC.BD, ∠BAD = α and ∠CAD = β then which one of the following is correct?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- Aα = β
- Bα = 2β
- C2α = β
- D2α = 3β
Explanation
AB·DC = AC·BD rearranges to AB/AC = BD/DC, which by the converse of the angle-bisector theorem means AD bisects ∠BAC. Hence ∠BAD = ∠CAD, i.e. α = β — option A.