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CAT 2002 — QA Question 19

Geometric CentersEasy

The internal bisector of an angle A in a triangle ABC meets the side BC at point D. AB = 4, AC = 3 and ∠A = 60°. Then what is the length of the bisector AD?

Answer & solution

  • 1237

  • B

    12137

  • C

    4137

  • D

    437

Solution

Area of âˆ†ADC = 12 AD × 3 × sin 30°

Area of âˆ†ADC = 12 AD × 4 × sin 30°

Area of âˆ†ADC = 12 × 3 × 4 × sin 60°

12 AD × 3 × sin 30° + 12 × AD × 4 × sin 30° = 12 × 3 × 4 × sin 60°

AD[3×12+4×12]=12×32

AD72=1232

∴ AD = 1237

Hence, option (a).