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| Math Central | Quandaries & Queries |
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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.
Penny
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