Need to find the radius

Any assistance much appreciated.

#Geometry

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Comments

Have tried in vain to find the radius.

Monty McGee - 3 years, 4 months ago

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.

Steven Yuan - 3 years, 4 months ago

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

Monty

Monty McGee - 3 years, 4 months ago

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

Dylan Valentine - 3 years, 3 months ago

Thanks for the reply.

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

Monty McGee - 3 years, 3 months ago

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.

Dylan Valentine - 3 years, 3 months ago

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.

Monty McGee - 3 years, 3 months ago

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

r = 6 +/- sqrt(10);

r = 6 - sqrt(10);

r = 2.84

G Silb - 3 years, 2 months ago

Ask Siri

Annie Li - 3 years, 4 months ago

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

Monty McGee - 3 years, 4 months ago

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

Annie Li - 3 years, 4 months ago

@Annie Li – Thanks.

Monty McGee - 3 years, 4 months ago

@Monty McGee – No probs. Just remember to thank Siri

Annie Li - 3 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$