Orthogonal Circles

Statement 1: Two orthogonal circles intersect to generate a common chord which subtends complimentary angles at their circumferences. Statement 2: Two orthogonal circles intersect to generate a common chord which subtends supplementary angles at their centers.

A variable line ax+by+c=0 , where a, b, c are in A.P. is normal to a circle (x-alpha)^2+(y-beta)^2=gamma , which is orthogonal to circle x^2+y^2-4x-4y-1=0 .The value of alpha + beta+ gamma is equal to

Angle of intersection of two circle and orthogonal intersection of circles

If a circle cuts orthogonally three circles, S_1 = 0, S_2=0, S_3=0 , prove that it cuts orthogonally and circle kS_1 + lS_2 + mS_3 = 0 .

x=1 is the radical axis of the two orthogonally intersecting circles. If x^(2)+y^(2)=4 is one of the circles, then the other circle, is

If a circle Passes through point (1,2) and orthogonally cuts the circle x^(2)+y^(2)=4, Then the locus of the center is:

Show that the locus of points from which the tangents drawn to a circle are orthogonal, is a concentric circle. Or Find the equation of the director circle of the circle x^2 + y^2 = a^2 .

Equation of the circle cutting orthogonal these circles x^(2)+y^(2)-2x-3y-7=0x^(2)+y^(2)+5x-5y+9=0 and x^(2)+y^(2)+7x-9y+29=0 is:

Illustration based upon Orthogonality Pole-Polar and Parametric Equation OF Circle

Illustration based upon Orthogonality Pole-Polar || Parametric Equation OF Circle