Math CentralQuandaries & Queries


Question from Carlos, a student:

Find the length of the radius of a circle in which a chord of length 6 units is twice as far from the center as a chord of length 12 units

Hi Carlos,

Draw a diagram.


The two chords in the diagram are of length 6 and 12 units so $|DE| = 3$ units and $|AB| = 6$ units. Suppose the radius of the circle is $r$ units and $|BC| = x$ units then $|EC| = 2x$ units. Triangles $CAB$ and $CDE$ are right triangles. Pythagoras can help at this point.


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