Circles and radii of 10cm and 12cm are in contact. Find the distance between

Circles and radii of 10cm and 12cm are in contact. Find the distance between the centers of the circles in cases of internal and external tangency.

Let us denote by the variable L the distance between the centers of the touching circles. Let us denote through the variable R1 the radius of the first circle equal to 10 cm, and through the variable R2 the radius of the second circle equal to 12 cm.

In the case of internal tangency, the distance between the centers of the touching circles is determined by the following formula.

L = R2 – R1.

Therefore, we obtain the following results.

L = 12 – 10.

L = 2 cm.

Thus, we find that in the case of internal tangency, the distance between the centers of the contacting circles is 2 cm.

In the case of external tangency, the distance between the centers of the touching circles is determined by the following formula.

L = R2 + R1.

Therefore, we obtain the following results.

L = 12 + 10.

L = 22 cm.

Thus, we find that in the case of external contact, the distance between the centers of the contacting circles is 22 cm.