Question

Construct a cyclic quadrilateral $ABCD$ with $AB=5cm,BC=4.3cm,\angle ABC={60}^{\circ }$ and diagonal $BD=5.6cm$. The length of the diagonal $AC$ (in $cm$) is :

Answer 1

$\Rightarrow$ Draw a line segment $AB=5cm$.

$\Rightarrow$ Construct an angle of ${60}^{\circ }$ at point $B$.

$\Rightarrow$ Cut off $BC=4.3cm$

$\Rightarrow$ Join $AC$.

$\Rightarrow$ Draw a perpendicular bisector on sides $AB$ and $BC$ meeting at point $O$.

$\Rightarrow$ Take $O$ as a center with radius $OA$ and draw a circle.

$\Rightarrow$ Take $B$ as a center with radius $BD=5.6cm$ and draw an arc on circle.

$\Rightarrow$ Join $BD,AD$ and $CD$.

$\Rightarrow$ Thus, $ABCD$ is a cyclic quadrilateral

$\Rightarrow$ We have to measure length of $AC$

$\Rightarrow$ $l\left(AC\right)=5cm$