Multiple choice

In a Δ ABC, AB = 9cm , BC = 12cm and CA = 6 cm. If AD, DM and DN are the angle bisector of ∠BAC, ∠ BDA and ∠ ADC respectively. If AM = 5.4cm then find the ratio of AD : AN.

  1. 5 : 13

  2. 5 : 12

  3. 12 : 5

  4. 13 : 5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a triangle with sides AB = 9 cm, BC = 12 cm, CA = 6 cm, we must first verify if such a triangle exists. The triangle inequality requires the sum of any two sides to exceed the third. Here: 9 + 6 = 15 > 12 (valid), 9 + 12 = 21 > 6 (valid), but 6 + 12 = 18 > 9 (valid). Actually, this triangle is valid. With AM = 5.4 cm given, and using angle bisector theorems, the ratio AD:AN can be calculated. The answer 13:5 is plausible given the geometry.

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