The chord length of the line where the common chord of circle C1: x ^ 2 + y ^ 2 = 1 and circle C2: x ^ 2 + y ^ 2-2x-2y + 1 = 0 is cut by circle C3: (x-1) ^ 2 + (Y-1) ^ 2 = 25 / 4 is () The answer to this question is 23 under the root Is there a simpler method, not so much calculation, I remember the teacher said

The chord length of the line where the common chord of circle C1: x ^ 2 + y ^ 2 = 1 and circle C2: x ^ 2 + y ^ 2-2x-2y + 1 = 0 is cut by circle C3: (x-1) ^ 2 + (Y-1) ^ 2 = 25 / 4 is () The answer to this question is 23 under the root Is there a simpler method, not so much calculation, I remember the teacher said

Circle C1: x ^ 2 + y ^ 2-1 = 0 and circle C2: x ^ 2 + y ^ 2-2x-2y + 1 = 0
The common chord equation is x + Y-1 = 0
The distance from C3 to chord is d = | 1 + 1-1 | / √ 2 = √ 2 / 2
The chord length cut by C3 is obtained by using chord length formula
MN=2√(R²-d²)=2√[25/4-(√2/2)²]=√23

High school mathematics problem: the equation of circle
(1) The center of the circle is on the straight line 5x-3y-8 = 0, and it is tangent to the coordinate axis. The equation (2) of the circle is solved, and the standard equation of the circle passing through the point a (0,4) B (4, b) and the center of the circle is on the straight line x-2y-2 = 0 is solved

In the plane rectangular coordinate system xoy, if the intersection points of the curve y = x2-6x + 1 and the coordinate axis are on the circle C, then the equation of the circle C is? Where do you know the x = 3 of the center coordinate of the circle?

Parabola y = x ^ 2-6x + 1, the axis of symmetry is x = 3, and there are two intersections (positive and negative 2 radicals 2 + 3,0) with X axis. If the circle passes through these two points, the line segment connecting the two points is the chord of the circle, and the straight line x = 3 perpendicular to this chord must pass through the center of the circle! Suppose that equation (x-3) ^ 2 + (y-b) ^ 2 = C, substitute the coordinates of the intersection into 8 + B ^ 2 = C, then replace c with B, and get equation (x-3) ^ 2 + (y-b) ^ 2 = C