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  • In Fig., if angle ACB = angle CDA, AC = 8 cm and AD = 3 cm, find BD.

In Fig., if \angle ACB = \angle CDA, AC = 8 cm and AD = 3 cm, find BD.

 

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Answer :

\left [ \frac{55}{3}\; cm\right ]

\text{Given : } \angle ACB=\angle CDA

AC = 8 cm and AD = 3 cm

\text{In} \Delta ACD\; and\; \Delta ABC

\angle A = \angle A    

\angle ADC = \angle ACB       

We know that if two angles of one triangle are equal to the two angles of another triangle, then the two triangles are similar by AA similarity criterion.

\therefore \; \; \; \; \Delta ADC\sim \Delta ACB

\Rightarrow \frac{AC}{AD}=\frac{AB}{AC}  \text{ [corresponding sides are proportional]}

=\frac{8}{3}=\frac{AB}{8}

AB=\frac{8 \times 8}{3}=\frac{64}{3}cm

BD+AD=\frac{64}{3}\; \; \; \; \; \; \; \; \; \; \; \left ( Q\; AB=BD+AD \right )

BD=\frac{64}{3}-AD

BD=\frac{64}{3}-3=\frac{64-9}{3}=\frac{55}{3}\; cm

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