2022 · Q77
The perpendicular AD on the base BC of a triangle ABC intersects BC at D so that DB = 3 CD. Which one of the following is correct?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A2 (AB + AC) (AB - AC) = BC²
- B3 (AB + AC) (AB - AC) = 2 BC²
- C4 (AB + AC) (AB - AC) = 3 BC²
- D5 (AB + AC) (AB - AC) = 4 BC²
Explanation
Put CD = x, DB = 3x. Then AB²−AC² = (AD²+9x²)−(AD²+x²) = 8x² = (AB−AC)(AB+AC). Hence 2(AB+AC)(AB−AC) = 16x² = BC². The keyed option is A.