Multiple choice

In $\displaystyle \bigtriangleup ABC$, BC is extends to D such that CD = AC. Length of angle bisector of C is 5 unit. If BC = 4 units and AC = 8 units. Find AD.

  1. 10 units

  2. 15 units

  3. 20 units

  4. 12 units
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B Correct answer
Explanation

Using the Angle Bisector Theorem and properties of triangles, the length of the angle bisector of C in triangle ABC is given by 2*AC*BC*cos(C/2)/(AC+BC). With AC=8, BC=4, bisector=5, we find cos(C/2). Then use the Law of Cosines to find AB, and subsequently AD.

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