# Geometry

determine the radius of a circle if a 24 inch chord is 9 inches from the center

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1. Use the intersection chord property:
if two chords intersect, each subdivided into segments a,b and c,d respectively, then ab=cd.

Here, draw a diameter (which is also a chord of total length 2r) that intersects the given chord at right angles.
The 2 segments of the given chord are then a=b=12".
The diameter's segments are then
c=r+9 and d=r-9.
Thus (r+9)(r-9)=12²
r²-9²=12²
r²=144+81=225
r=15

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2. 15

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