Two circles of diameters 18 cm and 22 cm are such that the distance between their centres is 29 cm. What is the length of the tangent to the circles that intersect the line joining the centre?

For two circles with radii r1=9 cm, r2=11 cm, and distance between centers d=29 cm, the length of the common tangent (external) is given by sqrt(d^2 - (r1+r2)^2) = sqrt(29^2 - 20^2) = sqrt(841 - 400) = sqrt(441) = 21 cm. This uses the Pythagorean theorem on the right triangle formed by the line of centers and the tangent.