Fox 353

Tony García‏ from Dominican Republic submitted this one.  It looks like it requires brute force.  Better than being idle I guess!  So enjoy...

The answer is not confirmed yet.

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Fox 352

We will add comments later...

There are many lazy observations that could help.

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Fox 351

Let's start with this simple one for high-schoolers :)

Pure-geometric solution will be appreciated.

We'll build upon this later.

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Fox 350

Based on the evidence presented by Bleaug, this is updated as follows:

Thank you.

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Fox 349

This is just one step forward to the general case. Should not be very hard unless the claim is wrong :)

Yes, a geometric solution will be appreciated...

Fox 348

We'll return back to Sampy's question later. But, for a change let's see a simple one - or at least it looks simple. We're looking for the shortest proof of the claim below. May be purely-geometric one? Or is the claim wrong? Let us know...

Fox 347

Below is the general case submitted by Roland Sampy.
There seems to be at least 2 expressions for r.
We had a solution, but it looked a little clumsy. Moreover, we lost it :)

So, do help us to recover... Oh yes, do enjoy as well...