Question

Construct a triangle whose sides are $4$cm, $6$cm and $8$cm. Draw the circumcircle of the triangle.

Answer 1

Steps for construction:

I) Construction of triangle

1) Let the base of the triangle be $QR=8$cm.

2) Taking Q as the centre and radius 4cm on the compass, draw and arc on the upper side of $QR$.

3) Taking R as the centre and radius 6cm on the compass, draw and arc on the upper side of $QR$, intersecting the previous arc. Mark this point of intersection as point P.

4) Join points P to Q and P to Q to complete the $△PQR$.

II) Construction of perpendicular bisectors

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

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

3) Join points $X$ and $Y$. This line $XY$ is the required perpendicular bisector of side $QR$.

4) Similarly, draw perpendicular bisectors of sides $PQ$ and $PR$.

III) Construction of circumcircle

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

Name that point as $O$.

2) Taking point O as the centre and OP as the radius draw a circle. Points Q and R should also lie on this circle.

3) This is the required circumcircle.