Statement 1 : The number of circles passing through (1, 2), (4, 8) and (0, 0) is one. Statement 2 : Every triangle has one circumcircle

Statement 1 : The number of circles touching lines x+y=1,2x-y=5, and 3x+5y-1=0 is four Statement 2 : In any triangle, four circles can be drawn touching all the three sides of the triangle.

The equation of the smallest circle passing through the point (1,0) and (0,1) is

Statement 1 : The number of common tangents to the circles x^(2) +y^(2) -x =0 and x^(2) +y^(2) +x =0 is 3. Statement 2 : If two circles touch each other externally then it has two direct common tangents and one indirect common tangent.

Statement-1: The centre of the circle passing through the points (0, 0), (1, 0) and touching the circle C : x^(2)+y^(2)=9 lies inside the circle. Statement-2: If a circle C_(1) passes through the centre of the circle C_(2) and also touches the circle, the radius of the circle C_(2) is twice the radius of circle C_(1)

Statement 1 : The center of the circle having x+y=3 and x-y=1 as its normals is (1, 2) Statement 2 : The normals to the circle always pass through its center

Find the equation of the circle which passes through the points (1,1), (0, -1) and (-2, 0)

Statement 1 : The number of common tangents to the circles x^(2) + y^(2) =4 and x^(2) + y^(2) -6x - 6y = 24 is 3. Statement 2 : If two circles touch each other externally thenit has two direct common tangents and one indirect common tangent.

A circle passes through (0,0) and (1, 0) and touches the circle x^2 + y^2 = 9 then the centre of circle is -

The centre of the circle passing through the points (0,0), (1,0) and touching the circle x^2+y^2=9 is

Statement - 1 : Equations (2 pm sqrt3) x - y = 1 pm 2sqrt3 represent two sides of an equilateral triangle having one vertex (2 , 3) and x + y - 2 = 0 as the opposite side . Statement - 2 : The equation of the lines passing through (x_(1) , y_(1)) and making constant angle alpha with the line y = mx + c are given by y - y_(1) = (m pm tan alpha)/( 1 pm tan alpha) ( x - x_(1))