CIRCLES | FAMILY OF CIRCLES, RADICAL AXIS, PROPERTIES OF RADICAL CENTER | Property 1: The equation of the family of circles passing through the point of intersection of two given circles ., Property 2: The equation of the family of circles passing through the point of intersection of line and circle, Property 3: The equation of the family of circles touching the circles and line at their point of contact is, Property 4: The equation of the family of circles passing through two given points `P(x_1,y_1) and Q(x_2,y_2)`, Property 5:The equation of family of circle which touches `(y-y_1)=m(x-x_1)` at `(x_1;y_1)` for any finite m is, Equation of a circle circumscribing a triangle whose sides are L1=0;L2=0 and L3=0, Introduction to Radical Axis, The coordinates of the radical center can be found by solving the equation `S_1=S_2=S_3, The radical center of the three circles described on the sides of a triangle as diameters is the orthocenter of a triangle., The radical center of three given circles will be the center of a fourth circle which cuts all the three circles orthogonally.