Question

Construct a cyclic quadrilateral $ABCD$ in which $AB=4cm,BC=5.6cm,AC=7.2cm$ and $AD=4.5cm$. Then, length of the other diagonal $BD$ is:

• A. $6.9cm$
• B. $4.5cm$
• C. $5.6cm$
• D. $7.7cm$

Answer 1

The correct option is A $6.9cm$

• 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 $ABCD$

$l\left(BD\right)=6.9cm$ (measurement)