Question

Construct the circumcircle of the triangle ABC in which AB=$5cm$, BC=$7cm$, and$\angle ABC = {60^0}$.

Answer 1

Hint-To construct a circumcircle of the triangle, first construct a triangle with the given measurement and then construct a circle.

Complete step-by-step answer:

        1) Steps for constructing triangle:
a.Let us take the base of triangle BC as $7cm$ and draw a line.
b.Now taking B as centre let us draw $\angle ABC = {60^0}$ with the help of a protractor and draw ray BX.
c.Let us measure a length of $5cm$ on the compass and with B as centre, mark a point A at $5cm$
From B on ray BX.
d.Now let us join points A and C to get triangle ABC.

    2) Steps of constructing perpendicular bisectors:
a.Here let us take B as centre and radius more than half of BC, mark the arcs below and above the line.
b.Now with centre A and using the same radius, let us mark the arcs below and above the line to intersect to already drawn arcs. Now let us name the new points as P and Q.
c.Here let us join P and the line PQ is the required perpendicular bisector of the both side of BC.
d.Similarly let us draw the perpendicular bisector of sides AB and AC.
    3) Steps for constructing the circumcircle:
a.All the perpendicular bisector of triangle ABC will intersect at one point in the interior of the triangle.
b.Let us name the point as O
c.Taking the point O as centre and OA as radius draw a circle. Here point B and C should lies on the circle
d.This is the required circumcircle of triangle.

NOTE: Please draw the length of the sides of the triangles to appropriate measurement to get a perfect circumcircle. The best way to construct the circumcircle of a triangle is first we have to construct the triangle by using the given measures. And then we construct the perpendicular bisectors followed by the circumcircle by following the steps to get a perfect measured circumcircle of triangle.