Question

Construct a cyclic quadrilateral XYZW in which WX$=3.5$cm, $\angle$X$={75}^o$, XY$=2.8$cm, and the vertex Z lies on the angle bisectors of $\angle$WXY.

Answer 1

• Draw a line segment $WX$ of length $3.5cm$
• From $X$, make an angle of ${75}^o$ and mark a point $Y$ at a distance $2.8cm$ from $X$
• Draw perpendicular bisector of $XY$ and $WX$. These bisectors meet at $O$
• Taking $O$ as center, draw a circle of radius $OX$
• Make angular bisector of $\angle WXY$. This bisector of angle cut the formed circle at $Z$
• Join $WXYZ$, would be the required quadrilateral.