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Find the radius of a circle with center at (4,1)
if a chord of length 4√2 is bisected at (7,4)
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Make a sketch.
In your sketch, find a right-angled triangle, which has the vertices OXY, where
O is the center of the circle; X is the midpoint of the chord and
Y is one of the two intersection points of the chord and the circle.
The leg XY of this triangle has the length , half of the leg
of the chord; the leg OX is the vector with coordinates (3,3) = (7-4,4-1).
The length of this leg OX is .
The radius "r" of the circle is the hypotenuse of this triangle
= + = 4*2 + 9*2 = 8 + 18 = 26.
ANSWER. The radius of the circle is r = units.
Solved.