Question

Construct the circumcircle of triangle $ABC$ in which $AB=5cm.BC=7cm$ and $\angle ABC={60}^o$.

Answer 1

Steps for construction:

I) Construction of triangle

1) Let the base of the triangle be $BC=7$cm.

2) With taking B as the centre, draw $\angle ABC={60}^o$ with the help of a protractor and draw ray $BX$.

3) Measure 5cm on your compass and with B as the centre, mark point A at 5cm from B on ray $BX$.

4) Join points A and C to get $△ABC$.

II) Construction of perpendicular bisectors

1) Taking $B$ as the centre and radius more than half of BC, mark arcs below and above the line.

2) Now, with $A$ as the centre and same radius, draw arcs above and below the line to intersect the already drawn arcs. Name the new points as $P$ and $Q$.

3) Join points $P$ and $Q$. This line $PQ$ is the required perpendicular bisector of side $BC$.

4) Similarly, draw perpendicular bisectors of sides $AB$ and $AC$.

III) Construction of circumcircle

1) All the perpendicular bisectors of $△ABC$ will intersect at one point in the interior of the triangle.

Name that point as $O$.

2) Taking point O as the centre and OA as the radius draw a circle. Points B and C should also lie on the circle.

3) This is the required circumcircle.