Two circles have diameters 8 cm and 6 cm. Which is correct? i. If the circles touch internally, the distance between their centres is 1 cm. ii. If the circles touch externally, the distance between their centres is 7 cm. iii. The sum of the perimeters of the two circles is 14π cm.

Jashore Board 2025

Two circles have diameters 8 cm and 6 cm. Which is correct?

i. If the circles touch internally, the distance between their centres is 1 cm.
ii. If the circles touch externally, the distance between their centres is 7 cm.
iii. The sum of the perimeters of the two circles is 14π cm.

Think it through first, then pick an option.

Answer and explanation

Correct answer: d i, ii and iii

All three are true: i gives 4 − 3 = 1, ii gives 4 + 3 = 7, iii gives π × 8 + π × 6 = 14π cm.

Why the other options are wrong

a i and ii: iii is true too: diameters 8 and 6 give perimeters 8π and 6π, which add to 14π; so i and ii alone are not enough.
b i and iii: ii is true too: external touching gives d = 4 + 3 = 7 cm; so i and iii alone are not enough.
c ii and iii: i is true too: internal touching gives d = 4 − 3 = 1 cm; so ii and iii alone are not enough.