Question 319456
Chord AB has gradient -6/2 or -3. Chord AC has gradient -8/4 or -2
Perpendicular lines therefore have gradients of 1/2 and 1/3 respectively.
The perpendicular will go through the mid point of the chord or (2,-1) and (3,-2)
The line going through(2,-1) with a gradient of 1/3 is y=1/3x -5/3
The line going through (3,-2) with a gradient of 1/2 is y = 1/2x - 7/2
re-arrange to 3y - x = 5 and 2y - x = 7
Solve simultaneously to get y = 2, which gives x = 11
So centre of circle is (11,2).
Point A is on the circumference, so the radius is (1,2) to (11,2) or 10.
The equation or the circle is thus (y - 2)^2 + (x - 11)^2 = 100