Math CentralQuandaries & Queries


Question from Lorraine, a student:

I cannot figure out this question:
There are two chords in a circle, an 8 inch chord and a 10 inch chord. The 8 inch chord
is twice the distance from the center as the 10 inch chord. What is the radius?
Can you help?
Thank you!

Hi Lorraine.

The distance from the center to a chord would meet the chord in at a right angle right at the midpoint of the chord.

If you draw this, and also draw the radii involved, you can see two distinct right triangles:


So let a = the distance to the 10 inch chord, then 2a is the distance to the 8 inch chord, according to the description.

Now take a look at what pythagoras has to say:

r2 = 52 + a2 and r2 = 42 + (2a)2

Can you solve this system of simultaneous equations for r?

Stephen La Rocque.

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