Question

Construct a cyclic quadrilateral $ABCD$ in which $AB=4cm,BC=5.6cm,AC=7.2cm$ and $AD=4.5cm$. If radius of the circle circumscribing the quadrilateral $ABCD$ is $r$. Then $5r=?$
(Round-off to the nearest integer)

Answer 1

• Draw a line segment $BC$ of length $5.6cm$.
  
• From $B$ make an arc of length $4cm$.
  
• From $C$ make an arc of length $7.2cm$.
  
• Both these arcs cuts each other at point $A$.
  
• Join $AB$ and $AC$.
  
• Draw perpendicular bisector of line $BC$ and $AB$. The perpendiculars intersect each other at $O$.
  
• Draw a circle of radius $OB$ from $O$ as center. This circle also touches $A,B$ and $C$.
• From $A$ mark an arc of $4.5cm$ on circle.
  
• Join $ABCD$

$r=\frac{a}{2\sin A}=\frac{BD}{2\sin \left({108}^o\right)}=\frac{6.9}{2\times \left(0.95\right)}=3.625r=18$