If wet up coordinates so that O directly below the center of AB.
and A is at x = -7 and B is at x=7
then C is at (-5,4)
segment AC has slope 2
The radius R is the perpendicular bisector of AC, so it has slope -1/2
If F is the midpoint of AC then F is at (-6,3), making O = (0,-1)
so R = 3√5
If G is the closest point on the circle to E, then G is where the circle intersects OE extended. That is, where
x^2 + (y-1)^2 = 45
y-1 = -1/5 (x+5)
Now just find the distance EG where E = (-5,1)
In circle O, perpendicular chords AB and CD intersect at E so that AE= 2, EB= 12 and CE= 4. Find the radius of circle O and the shortest distance from E to the circle.
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