Multiple choice

AD is the bisector of $\angle A$ of $\Delta ABC, AC =4.2 cm, DC =6 cm, BC = 10 cm$, then AB is:

  1. $2.8 cm$
  2. $3 cm$
  3. $3.5 cm$

  4. none of these
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A Correct answer
Explanation

By the Angle Bisector Theorem, AB/AC = BD/DC. Since BC = 10 and DC = 6, BD = 4. AB/4.2 = 4/6. AB = 4.2 * (4/6) = 4.2 * (2/3) = 2.8 cm.

AI explanation

Use the angle bisector theorem, which states that the bisector of an angle divides the opposite side in the ratio of the adjacent sides. First, find BD by subtracting DC from BC to get 4 cm, then set up the proportion AB divided by 4.2 equals 4 divided by 6. Solving this yields AB = 2.8 cm.

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