CDS 2026 (I) Elementary Mathematics, question 68

Topic: Geometry

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Q68

In a triangle ABC, AB=18AB=18 cm, BC=22BC=22 cm and AC=15AC=15 cm. The bisector of ∠BAC\angle BAC intersects BC at D. What is (BD×DC)(BD\times DC) equal to ?

  1. (a) 121 cm2121\text{ cm}^{2}
  2. (b) 120 cm2120\text{ cm}^{2}Correct answer
  3. (c) 117 cm2117\text{ cm}^{2}
  4. (d) 96 cm296\text{ cm}^{2}

Solution.

Answer: (b) 120 cm2120\text{ cm}^{2}

  1. By the internal angle-bisector theorem, BD/DC=AB/AC=18/15=6/5BD/DC = AB/AC = 18/15 = 6/5.
  2. Since BD+DC=22BD + DC = 22, the segments are 12 cm and 10 cm.