2026 · Q68
In a triangle ABC, AB = 18 cm, BC = 22 cm and AC = 15 cm. The bisector of ∠BAC intersects BC at D. What is (BD × DC) equal to?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A121 cm²
- B120 cm²
- C117 cm²
- D96 cm²
Explanation
By the internal angle-bisector theorem, BD/DC=AB/AC=18/15=6/5. With BD+DC=22, we get BD=12 and DC=10, so BD·DC=120 cm², option B. The product BD·DC=12·10=120 is unaffected by which segment is labelled BD or DC.