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Question

In the figure, if AC is bisector of BAD such that AB = 3 cm and AC = 5 cm, then CD =


A

2 cm

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B

3 cm

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C

4 cm

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D

5 cm

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Solution

The correct option is C

4 cm


In the figure, AC is the bisector of BAD,

AB = 3 cm, AC = 5 cm

In ΔABC and ΔADC,

AC=AC (Common)

B=D (Each 90)

BAC=DAC

( AC is the bisector of A)

ΔABC ΔADC (AAS axiom)

BC=CD and AB=AD (c.p.c.t.)

Now in right ΔABC,

AC2=AB2+BC2

(5)2=(3)2+BC2

25=9+BC2 BC2=259=16=(4)2

BC=4 cm

But CD=BC

CD=4 cm


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