The discussion focuses on finding the equation of the smallest circle that contains three given circles defined by their equations. The circles provided are: 1. x² + y² - 4y - 5 = 0, 2. x² + y² + 12x + 4y + 31 = 0, and 3. x² + y² + 6x + 12y + 36 = 0. The centers of these circles are located at (0,2), (-6,-2), and (-3,-6) with a radius of 3 for each. The solution involves calculating the circumcenter of the triangle formed by the centers of the circles, which will be equidistant from all three vertices, and then determining the radius of the containing circle as the distance from the circumcenter to any center plus the radius of the circles.
PREREQUISITESStudents studying geometry, mathematicians focusing on circle properties, and anyone tackling problems involving multiple circles in coordinate systems.
I think you misunderstood the problem.Angry Citizen said:What are the equations? There is an easy way to tell which is the 'smallest' circle given the equations. Hint: Look at the constants, especially the one after the minus sign in the radical.
The problem is very difficult to solve if the circles don't have some special relationship such as they are all touching at one point each for example.phymatter said:Homework Statement
if equation of 3 circles is given then find the equation of the smallest circle containing all 3 circles
Homework Equations
The Attempt at a Solution
i can do this question for 2 circles , please give a hint for 3 circles
Suk-Sci said:The triangle is an equilateral triangle...circumcentre is same as centroid...
Remember the centroid ratio and pythagoras theorem...
I hope this will help you!
Thanx...
Suk-Sci