Find distance between intersections of circle and line?

[Albert Chan]

Midpoint of intersecting points is closest to the circle center, (-1,0), a line with slope -1/2

y = 2x + 3
y = -1/2*x -1/2 ; line passes circle center and midpoint
-> midpoint = (-1.4, 0.2)

Distance from midpoint to circle center = √(0.4² +0.2²) = √(20)/10 ~ 0.447
Distance from midpoint to intersecting points= √(55 - 20/100) = √(274/5) ~ 7.403

Distance between intersecting points ~ 2 * 7.403 ~ 14.8

Intersecting points = (-1.4 ± t, 0.2 ± 2t) for some t

t² + (2t)² = 5 t² = 274/5; matching distance square
t = ±√(274)/5

-> Intersecting points ~ (-1.4 ± 3.31, 0.2 ± 6.62) = (-4.71, -6.42) and (1.91, 6.82)