Three circles of radii 1 cm, 2 cm and 3 cm are drawn so that each one touches the other two externally. What kind of triangle is formed by joining the three centres?

When two circles touch externally the point of contact lies on the line of centres, so the distance between two centres is just the sum of those two radii. The three sides are therefore 1 + 2 = 3 cm, 2 + 3 = 5 cm and 3 + 1 = 4 cm. Since $3^2+4^2=9+16=25=5^2$, the converse of Pythagoras makes the triangle right-angled, with the right angle at the centre of the 1 cm circle. It is scalene, so it is neither equilateral nor isosceles, and it cannot be obtuse because the squares balance exactly rather than tipping over.