BrainDen.com - Brain Teasers

## Question

A square sits on the diameter of a circle with one corner touching it, as shown. Given the area A of the square and the distance x from its touching edge to the far end of the diameter, find the circle's radius. ## Recommended Posts

• 2

I'm thinking the length of the radius is .5(x+(y^2)/x).

Again I'm posting from my phone as my laptop needs to charge. I'll show my work when I get a chance to plug it in.

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Oops! In that formula

y^2 should be A. I was working stuff out separately and for got to put the sqrt(A) back in.

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• 1

I no longer remember whether I ever knew this, but...

Since I haven't learned how to send you a picture,
Let's name some coordinates:
* m = left end of the diameter
* n = right end of the x-length segment on the diameter
* p = touching corner of the square
* q = right end of the diameter

and let's name some lengths:
* s = sqrt(A),
* t = distance from n to q

I don't remember whether this is true, but
IF the angle formed by mpq is a right angle, then
triangle (mnp) is similar to triangle (npq)
and

x/s = s/t
t = s^2/x = A/x
radius = (x + A/x) / 2

So, I've caught up with Rob

Edited by CaptainEd
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Radius = (x squared + A)/2x

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