Question

Construct a cyclic quadrilateral $XYZW$ such that $XY=4.8cm,YZ=6.4cm,\angle ZXY={25}^{\circ }$ and $\angle XZW={40}^{\circ }$. Then, radius of the circumcircle of the cyclic quadrilateral is:

• A. $3.8cm$
• B. $7.6cm$
• C. $5.9cm$
• D. $8.4cm$

Answer 1

The correct option is B $7.6cm$

• Draw a line segment $XY$ of length $4.8cm$
• From $X$, draw a line at ${25}^o$ from $XY$.
  
• From $Y$ mark an arc of length of $6.4cm$. The arc cuts the line at ${25}^o$ from $XY$ at $Z$.
  
• These perpendiculars intersect each other at $O$.
  
• Taking $O$ as center, draw a circle of radius $OX$. This circle touches $X,Y$ and $Z$.
• From $Z$ draw a line at angle of ${40}^o$ with base $XZ$. This line cuts the circle at point $W$.
  
• Join $XYZW$

We know, $R=\frac{a}{2\sin A}$

In $△WXZ,\angle WZX={40}^o$ (given)

$WX=9.8cm$ (measurement)

$R=\frac{9.8}{2\sin {40}^o}=7.6cm$