First You with simple algebraic steps write each equation in the form...
... and then find a with the well known quadratic equation resolution formula...
- the circles are congruent
- common tangent of both circles is the line y = x
- each circle is the image of the other circle by reflection over the line y = x
- the distance between the centers equals the diameter of one circle
Solve for a:
According to the text of the question both circles have the same radius. I tried to find two congruent circles where one circle touches the other internally. To be honest I wasn't very successful.If there are two circles such that and touch each other,
Then what can I write for " a = ? "
To be exact you have to consider 3 cases:
1. a > b, that means the circle with M(a, b) is placed below the line y = x
2. a = b, that means both circles have the same midpoint on the line y = x (and only in this case there could be an internal touching)
3. a < b, that means the circle with M(a, b) is placed above the line y = x
I've used only the first case because the 3rd case is the reflection of the 1st case over the line y = x.