The radical axis turns an apparently complicated problem into one that is already known.
Observation — The procedure
To find the intersection points of two circles it is therefore enough to:
- subtract their equations to obtain the radical axis, which is a line;
- set up the system of this line with one of the two circles;
- solve the system (one first-degree equation, the other second-degree, hence easy).
This method turns a circle-circle intersection problem into a line-circle intersection problem.
At step 2, it is convenient to choose the circle with the simpler equation to reduce the calculations.
Links
Topics: Circonferenza analitica
Concepts: Asse radicale · Intersezione circonferenze · Intersezione retta circonferenza
Methods: Circonferenza intersezione
Skills: Geometria analitica · Risolvere sistemi