Question

In the given figure, if $\angle ACB=\angle CDA,AC=8cm$ & $AD=3cm$, then find $BD$.

Answer 1

Given: $\angle ACB=\angle CDA$

$AC=8cm$

$AD=3cm$

In $△ABC,\angle CDA={90}^{\circ }$ [given]

$\therefore \angle ACB={90}^o$

From $△ACD,\cos A=\frac{AD}{AC}=\frac{3}{8}$

But from $△ABC,\cos A=\frac{AC}{AB}$

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

$\Rightarrow AB=8cm$

Then $BD=AB-AD$

$=8-3$

$=5cm$