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In ∆ABC, AD is the bisector of ∠A meeting side BC at D. Find the length of CD. Hint: Set up a proportion and solve for x, then find the length of CD.

In ∆ABC, AD is the bisector of ∠A meeting side BC at D. Find the length of CD. Hint-example-1

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The length of the segment CD is 39 centimeters.

What are angle bisectors?

Angle bisectors are lines that cut across the angle under consideration. The term "bisect" means to divide into two equal portions. The considered angle is therefore divided in half by the bisected halves.

Given:

In ∆ABC, AD is the bisector of ∠A meeting side BC at D.

AC = 13 cm, AB 7 cm.

By the angle bisector theorem,

13/3x = 7/(2x -5)

13(2x -5) = 21x

26x - 65 = 21x

5x = 65

x = 13.

The length of the segment CD is 39 centimeters.

Therefore, CD = 39 cm.

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