Question

Construct a cyclic quadrilateral $PQRS$ such that $PQ=QR=4.3cm$ and diagonals $PR=6.2cm,QS=5.8cm$. Then the perimeter of the cyclic quadrilateral is:
(Round-off to the nearest integer)

Answer 1

• Draw a line segment $QR$ of length $4.3cm$.
  
• From $Q$ make an arc of length $4.3cm$.
  
• From $R$ make an arc of length $6.2cm$.
  
• Both these arcs cuts each other at point $P$.
  
• Join $PQ$ and $PR$.
  
• Draw perpendicular bisector of line $PQ$ and $QR$. The perpendiculars intersect each other at $O$.
  
• Draw a circle of radius $OQ$ from $O$ as center. This circle also touches $P,Q$ and $R$.
• From $Q$ mark an arc of $5.8cm$, this arc cuts the circle at point $S$
  
• Join $PQRS$, is the required quadrilateral.
  

Given, $PQ=QR=4.3cm$

$PS=2.6cmRS=5.6cm$

Perimeter $=PQ+QR+RS+PS=16.8=17$