Draw circles with centres A, B and C each of radius 3 cm, such that each circle touches the other two circles.

Explanation:-

We are given that the radius of each circle is 3 cm. According to the property of circles that when two circles touch each other externally, then the distance between their centers is equal to the sum of their radii. Therefore, the distance between the centers of two circles is 3 cm + 3 cm = 6 cm. Similarly, the distance between the centers of the third circle and the other two circles is also 6 cm.

To construct the circles, we draw a line segment AB of length 6 cm. With A as the center and a radius of 6 cm, we mark an arc. Then, with B as the center and a radius of 6 cm, we mark an arc intersecting the previously drawn arc at point C. We join AC and BC to complete the triangle ABC.

Next, we draw three circles with centers A, B, and C, and radii of 3 cm each. It can be observed that each circle touches the other two circles externally, as required.

Therefore, the construction of the circles with the given properties is complete.