The radius of the two circles is 3cm and 4cm and the distance between their centers is 5cm.

The radius of the two circles is 3cm and 4cm and the distance between their centers is 5cm. Do these circles have common points?

Circles are given:
circle 1 with center at point О₁ and radius R1 = 3 cm;
circle 2 centered at point O₂ and radius R2 = 4 cm;
distance О₁О₂ = 5 cm.

Depending on the distance between the centers of the circles (segment О₁О₂), there are three options for the relative position of the circles.
1) The centers are located far away, i.e. О₁О₂> R1 + R2.
In this case, the circles have no common points.

2) The distance between the centers and the sum of the radii are O₁O₂ = R1 + R2.
In this case, the circles touch and have one common point.

3) The centers are located close, i.e. О₁О₂ <R1 + R2.
In this case, the circles intersect and have two common points.

In our case
О₁О₂ <R1 + R2
5 <3 + 4
5 <7

This means that the circles have two common points.