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Hint 2: Let $O$ be the center of the circle and $X$ be the point where the rectangle touches the circle. Create a right triangle with $OX$ as the hypotenuse and whose side lengths you can easily find.

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

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## Comments

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TopNewestHave tried in vain to find the radius.

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Hint 1:Try forming a right triangle.Hint 2:Let $O$ be the center of the circle and $X$ be the point where the rectangle touches the circle. Create a right triangle with $OX$ as the hypotenuse and whose side lengths you can easily find.Log in to reply

Thanks, Steven. I tried that before but obviously did not hit upon the correct setup; will go at it again.

Monty

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You are assuming that rectangle touches the circle, when the illustration shows that it doesn't.

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Thanks for the reply.

That's my fault; I didn't draw it correctly. The rectangle is indeed supposed to be touching the circle.

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I don't think there is enough info to solve the problem. That's not a circle, it's an oval. It's wider than it is tall. It won't have 1 radius.

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Thanks for the reply.

The drawing is not correct; I didn't draw it correctly with the Word drawing tool; it is supposed to be a circle.

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sqrt [ r^2 - (r-1)^2 ] + r = 5;

r = 6 +/- sqrt(10);

r = 6 - sqrt(10);

r = 2.84

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Ask Siri

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Hi Annie. Thanks for the comment. Who is Siri ?

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Oh know, the apple help system. Here is some information about it: Siri

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