Question

Construct a cyclic quadrilateral ABCD in which AB$=3.4$cm, BC$=3$cm, $\angle$B$={96}^o$ and the vertex D lies on the perpendicular bisector of BC.

Answer 1

• Draw a line segment $AB$ of $3.4cm$
• From vertex $B$ and base $AB$ make an angle of ${96}^o$
• Mark a point $C$ of length $3cm$ from $B$ at angle ${96}^o$
• Draw perpendicular bisectors of $AB$ and $BC$
• These bisectors meet at point $O$
• Taking $O$ as center, draw a circle of radius $OB$
• The circle intersects perpendicular bisector of $BC$ at $D$
• Join $ABCD$. The figure formed is the required quadrlateral.