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

Consider the following statements I.Number of circles touching the given three non- concurrent lines is 4. II.Number of circles passing through (1,2),(4,8) and (0,0) is one. Which of the above statement(s) is/are correct?

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 number of circle having radius 5 and passing through the points (-2,0) and (4,0) 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)

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

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