In the adjacent figure, if two circles are equal and the third was of radius 4 units, find the radius of equal circles.

1. Break Down the Problem

To find the radius of the two equal circles, we can assume that the system involves some relationship between the circles, possibly using the properties of tangents or the geometry of the arrangement of the circles.

2. Relevant Concepts

If two circles are equal and tangent to a third circle, we can use the formula for the relationship between the radii of tangent circles. If $r_1$ is the radius of the first circle (4 units), and $r_2$ is the radius of each of the equal circles, we often use the following relationship for exterior tangents: $r_1 + r_2 = d$ where $d$ is the distance between the centers of the circles. If they are internally tangent, we can use: $|r_1 - r_2| = d.$

3. Analysis and Detail

Assuming that the two equal circles are tangent to the larger circle, the relationship would imply that:

1. If they are externally tangent, $4 + r_2 = d$

2. If they are internally tangent, $|4 - r_2| = d$

In this case, since we are not provided with the exact arrangement or distance, we can typically conclude based on symmetry and the nature of such problems that $d$ is most likely the sum of the radii for external tangents, hence: $r_2 = 4.$

4. Verify and Summarize

Since we concluded $r_2 = 4$ units based on the assumption of external tangency, if the circles are equal and both position along a similar axis, the radius of the equal circles is also 4.

Final Answer

The radius of the equal circles is 4 units.