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2026 · Q74

In a triangle ABC, AD is the bisector of angle A that meets BC at D. If AB = 21 cm, DC = 20 cm and AB : AC = 3 : 4, then what is AC² − BD² equal to?

Elementary MathematicsGeometry: Lines, Angles and Triangles
  1. A441
  2. B559
  3. C588
  4. D784

Explanation

By the angle-bisector theorem, BD/DC = AB/AC = 3/4, so BD = 20·3/4 = 15 cm. From AB : AC = 3 : 4 with AB = 21, AC = 28 cm. Then AC² − BD² = 784 − 225 = 559, option B.