Question

Draw a square of sides 5 centimetres and draw its circumcircle and incircle.

Answer 1

A square with side 5 cm as length can be drawn as follows:

1) Draw a line segment AB of length 5 cm.

2) At point A and B, draw ∠XAB = ∠YBA = 90°.

3) Taking A and B as the centres and 5 cm as the radius, draw arcs on rays AX and BY. Name the point of intersection as D and C.

4) Join DC.

Quadrilateral ABCD is the required square.

The incircle of this square can be drawn 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 AB. Name the point where it intersects AB as P.

3) With O as centre and OP 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 square.

The circumcircle for the given square can be constructed as follows:

1) Draw perpendicular bisectors of AB and BC. Let them intersect at point O.

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

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