Finding Equation of Smallest Circle Containing 3 Circles

[phymatter]

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

 

[Angry Citizen]

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.

 

[Mentallic]

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.

I think you misunderstood the problem.

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

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]

the given equations are :
1. x² +y² -4y-5 = 0
2. x² +y² + 12x +4y +31 = 0
3. x² +y² +6x +12y +36 = 0

the centres are (0,2) ; (-6,-2) ; (-3,-6) and radius of all is 3

 

[Mark44]

I haven't worked this through, but I believe what you need is the circumcenter of the triangle formed from the centers of the three circles. That point would be equidistant from the three vertices of the triangles, so that would be the center of the circle that surrounds the three given circles. After you know the coordinates of the circumcenter, you can find the distance, call it d, to any of the centers of the three given circles. The radius of your containing circle will be d + 3.

 

[Suk-Sci]

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

 

[phymatter]

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

thanks Suk-Sci !