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In the figure, \overline{A B} \perp \overline{C D}, and AD is the bisector of ∠BAE. AB = 4 cm and AC = 5 cm. Find CD.

Option: 1

10 cm


Option: 2

12 cm


Option: 3

15 cm


Option: 4

none of these


Answers (1)

best_answer

Let BD be x cm.

Given AB = 4 cm, AC = 5 cm and ∠ABC = 90°

therefore BC = 3 cm

\left [\because AC^2=AB^2+BC^2 \right ]

And also given, AD is the bisector of ∠ BAE.

Therefore, by vertical angle bisector theorem.

\\\frac{A B}{A C}=\frac{B D}{C D} \Rightarrow \frac{4}{5}=\frac{x}{3+x}\\\Rightarrow 12+4x=5x\\x=12

CD = 12 + 5 = 15 cm

Posted by

Suraj Bhandari

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