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Angle bisector theorem

CMAT 2019 · Quantitative Techniques & Data Interpretation · Easy · Geometry

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In a triangle ABCABC, ADAD is the bisector of angle AA. If AC=4.2 cmAC = 4.2\text{ cm}, DC=6 cmDC = 6\text{ cm}, BC=10 cmBC = 10\text{ cm}, find ABAB.

  1. A.

    2.7 cm

  2. B.

    2.9 cm

  3. C.

    2.8 cm

  4. D.

    3.4 cm

Answer

C

Explanation

By Angle Bisector Theorem: BDDC=ABAC\frac{BD}{DC} = \frac{AB}{AC}

Given BC=10 cm,DC=6 cm  ⟹  BD=10−6=4 cmBC = 10\text{ cm}, DC = 6\text{ cm} \implies BD = 10 - 6 = 4\text{ cm}. 46=AB4.2  ⟹  AB=4×4.26=2.8 cm\frac{4}{6} = \frac{AB}{4.2} \implies AB = \frac{4 \times 4.2}{6} = 2.8\text{ cm}

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