Question

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

• A. $12.9cm$
• B. $13.5cm$
• C. $10.4cm$
• D. $11.2cm$

Answer 1

The correct option is C $10.4cm$

• 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 $XYZW$

Length of shorter diagonal $=10.4cm$ (measurement)