Question

Use ruler and compass only for the following question. All construction lines and arcs must be clearly shown.
Construct a $△ABC$ in which $BC=6.5cm,\angle ABC={60}^{\circ },AB=5cm$. Construct a locus of points $l_1$ at a distance of $3.5cm$ from $A$. Also, construct a locus of points $l_2$ which is equidistant from $AC$ and $BC$. Let $l_1$ intersect $l_2$ in two points $X$ and $Y$. Measure $XY$.

Answer 1

1. Draw base $BC$ of length $6.5cm$. Make an angle of ${60}^{\circ }$ from $B$.

2. Mark an arc of radius $5cm$ from $B$ on the ${60}^{\circ }$ angle created and name it as $A$. Join $A-C$. $△ABC$ is the required triangle.

3. Draw a circle with centre as $A$ and radius $3.5cm$. This is the locus of the points equidistant from $A$ at a distance of $3.5cm$.

4. Draw the angle bisector of $\angle ACB$ which will be the locus of points equidistant from $AC$ and $BC$,

5. Measure the length of $XY$ which comes out to be $5cm$.