Question

Construct a $△ABC$ is which base $BC=5.5$ cm, $\angle A={60}^{\circ }$ and the medium $AB$ from the vertex $A$ is $4.5$ cm.

Answer 1

Construction:
$1.$ Draw a line segment $BC=5.5$ cm
$2.$ Through $B$ draw $BX$ such that $\angle CBX={60}^{\circ }$
$3.$ Draw $BY\perp BX$.
$4.$ Draw $\perp$ are bisector of $BC$ so that it cuts $BC$ at $M$ and $BY$ at $O$.
$5.$ Draw a circle with centre $O$ and radius $OB$.
$6.$ The major are $BKC$ of the circle contains the vertical angle ${60}^{\circ }$.
$7.$ With $M$ as centre, draw an arc of radius $4.5$ cm meeting the circle at $A$ and $A^{\prime }$.
$8.$ $△ABC$ or $△A^{\prime }BC$ is the require triangle.