Question

Construct $△LMN$ such that $LM=6.6$ cm, $\angle LNM={65}^{\circ }$, where $ND$ is median and $ND=5$ cm

Answer 1

1. Draw a base $LM$ of length $6.6cm$. Draw the perpendicular bisector of $LM$ and mark the midpoint as $D$.

2. From $L$ and $M$, draw angles of ${90}^{\circ }-{65}^{\circ }={25}^{\circ }$ and let them intersect the perpendicular bisector at $O$.

3. From $O$, draw a circle with radius $OM$.

4. Take any point $N$ on the circle and join $L-N$ and $M-N$.

$△LMN$ is the required triangle.