Two circles touch each other externally. The sum of their areas is (130\pi) cm2, and the distance between their centers is 14 cm. What will be the radii of the circles?

For externally touching circles, distance between centers equals sum of radii: r1 + r2 = 14. Areas: pi*r1^2 + pi*r2^2 = 130*pi, so r1^2 + r2^2 = 130. Using (r1+r2)^2 = r1^2 + r2^2 + 2*r1*r2: 14^2 = 130 + 2*r1*r2, giving 196 - 130 = 2*r1*r2, so r1*r2 = 33. The factors of 33 that sum to 14 are 11 and 3. Check: 11+3=14, 11^2+3^2=121+9=130. Option B (9+4=13 not 14), C (8+5=13), D (9+5=14 but 81+25=106).