Multiple choice

If AD is bisector of interior $\angle$ A of a triangle ABC and $AB =10 cm, AC =6 cm, BD =12 cm$, then $CD =$ ?

  1. $8$ cm
  2. $7.2$ cm
  3. $10$ cm
  4. $16$ cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

By the Angle Bisector Theorem, the ratio of the sides AB/AC equals the ratio of the segments BD/CD. So, 10/6 = 12/CD. CD = (12 * 6) / 10 = 7.2 cm.

AI explanation

By the Angle Bisector Theorem, the bisector of an interior angle of a triangle divides the opposite side in the ratio of the adjacent sides, giving AB / AC = BD / CD. Substituting the given values results in 10 / 6 = 12 / CD. Cross-multiplying yields 10 times CD = 72, which means CD = 7.2 cm.

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