A problem by Steven Yuan called "Three Lines, Three Circles"

Calvin edit: This post has been locked so that the discussion stays on the problem. If you can help, please make a comment in the solution discussion. Thanks!

Steven, I'm going to refer to you. This question is for you or anyone who knows the answer.

$r_a$ is the radius of excircle A. The proof of your problem uses the formula

$r_a r_b + r_b r_c + r_c r_a = s^2$

I have no doubt that the formula is true but I would very much like to see a proof of it.

By the way, I really enjoyed this problem. Keep up the good work.

#Geometry

Easy Math Editor

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Comments

@Steven Yuan FYI

Calvin Lin Staff - 6 years, 3 months ago

Michael, I would prefer that discussion of problems stay on the problem, so that others with a similar concern as yours may learn from it, instead of having to discover this other note.

As such, I have made a comment in the problem, and closed this note out. Thanks

Calvin Lin Staff - 6 years, 3 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}`	$\boxed{123}$