Math CentralQuandaries & Queries


Question from Tim:

Can I find the radius of a circle, if I have a chord of 2400mm, and a depth between the center of the chord and the perimeter of the circle of 150mm ?

Hi Tim,

In the diagram below triangle ADC is a right triangle and the length of CD is (r - 150) mm.

circle and chord

Pythagoras theorem gives you

\[1200^2 + (r - 150)^2 = r^2\]

Expanding the left side gives

\[1200^2 + r^2 - 300 r + 150^2 = r^2\]

Simplifying gives

\[300 r = 1200^2 + 150^2 = 1462500\]

and hence

\[r = \frac{1462500}{300} = 4875 \mbox{ mm}\]


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