In the image, it looks like we have two circles, each with a radius of $5$, and they appear to intersect at point $A$. Points $O$ and $B$ are the centers of the two circles, respectively.

The problem specifies:

• $OA = OB = 5$
• $OD = DA = DB$

We need to find the length of $AB$, which is the distance between the centers of the two circles, points $O$ and $B$.

Solution Outline

Since $OA = OB = 5$, this implies that each circle has a radius of $5$. Additionally, point $A$ is a common point on both circles, suggesting they intersect such that the line $AB$ (the distance between the centers) can be found as a straight line connecting $O$ and $B$.

Given the setup, $AB = OA + OB$ because both circles are tangent to each other at $A$. Therefore, we have: $AB = 5 + 5 = 10$

Final Answer

$AB = 10$

Would you like further details or have any questions?

Related Questions

1. What is the distance between the centers of two circles that do not intersect?
2. How would the solution change if $OA \neq OB$?
3. What is the formula to find the area of overlap between two intersecting circles?
4. How can you determine if two circles intersect based on the distance between their centers?
5. How would you solve if the problem involved three intersecting circles?

Tip

For problems involving intersecting circles, always check if the circles are tangent, overlapping, or separate to decide on the distance between their centers.