Question

Draw an equilateral triangle of sides 6 centimetres and draw its incircle and circumcircle.

Answer 1

An equilateral triangle with side 6 cm can be constructed as follows:

1) Draw a line segment AB of length 6 cm.

2) Taking A as the centre and 6 cm as the radius, draw an arc on the upper side of AB.

3) Taking B as the centre and 6 cm as the radius, draw an arc cutting the previously drawn arc at point C.

4) Join AC and BC.

ΔABC is the required equilateral triangle.

The incircle for the given equilateral triangle can be constructed as follows:

1) Draw angle bisectors of ∠A and ∠B. Let them intersect at point O.

2) With O as the centre, draw OK perpendicular to AC. Name the point where it intersects AC as D.

3) With O as the centre and OD as the radius, draw a circle. The circle so drawn touches all the sides of the triangle.

The given figure shows the required incircle of the given triangle.

The circumcircle for the given equilateral triangle can be constructed as follows:

1) Draw perpendicular bisectors of AB and AC. Let these perpendicular bisectors intersect at point O.

2) With O as the centre and radius OA = OB = OC, draw a circle passing through the points A, B and C.

The given figure shows the required circumcircle of the given triangle.