Question

Three circles of radii 3 cm, 4 cm and 5 cm touch each other externally. Find the perimeter of triangle formed by joining the centres of these circles.

Answer 1

When the three circles touch externally, the sides of the centre-triangle equal the sum of their respective radii.

The sides of the triangle formed by joining the centers are:

Side between centres of circles with radii 3 and 4:

 = 3 + 4 = 7 cm.

Side between radii 4 and 5:

= 4 + 5 = 9 cm.

Side between radii 3 and 5:

 = 3 + 5 = 8 cm.

Perimeter of the triangle:

= 7 cm + 9 cm + 8 cm

= 24 cm.