The radii of the two circles are 3cm and 5cm, and the distance between the most distant points of these circles is …

The radii of the two circles are 3cm and 5cm, and the distance between the most distant points of these circles is a) 18cm; b) 16cm; c) 13cm; d) 8cm;

1. The most distant points of two circles are on a straight line drawn through the centers of these circles. The distance between these points is:

AB = O1O2 + R1 + R2.

2. Knowing this distance and the radii of the circles, we can determine the distance between the centers:

R1 = 3;

R2 = 5;

O1O2 = AB – (R1 + R2);

O1O2 = AB – (3 + 5);

O1O2 = AB – 8.

a) AB = 18;

O1O2 = AB – 8 = 18 – 8 = 10 (cm).

b) AB = 16;

O1O2 = AB – 8 = 16 – 8 = 8 (cm).

c) AB = 18;

O1O2 = AB – 8 = 13 – 8 = 5 (cm).

d) AB = 18;

O1O2 = AB – 8 = 8 – 8 = 0 (cm), (the centers coincide).

Answer: a) 10 cm; b) 8 cm; c) 5 cm; d) 0.