the nearest point, the end of the chord, and the end of a diameter (opposite the point) form a right triangle
the half of the chord forms the altitude of the triangle
4 / 7 = 7 / (d - 4)
solve for the diameter (which is twice the radius)
a piece of a broken circular gear is brought into a metal shop so that a replacement can be built. a ruler is placed across two points on the rim, and the length of the chordd is found to be 14 inches. the distance from the midpoint of this chord to the nearest point on the rim is found to be 4 inches. find the radius of the original gear.
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