Roland Sampy has submitted this problem.

It looks right, but not confirmed yet.

Labels:
circle,
equilateral triangle,
proof

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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.

Labels:
Brute force,
Tangent,
Trigonometry

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Labels:
equilateral triangle,
proof

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

Pure-geometric solution will be appreciated.

We'll build upon this later.

Labels:
equilateral triangle,
simple proofs

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

Labels:
Area of a Triangle,
areas,
Counterexample,
proof,
Quadrilateral

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

Labels:
areas,
proof,
simple proofs,
Trapezoid

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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...

Labels:
Aint gonna happen,
simple proofs,
Trapezoid

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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 :)

There seems to be at least 2 expressions for

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...

Labels:
chords,
circle,
General Case

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Wooow... This has been quite long time, huh? Life makes people busy (although that is not the exact excuse.)

Is everybody alive? What have been up to? Bleaug? Newzad? Polar Fox ?? ...

The following fox is a simplified version submitted by Roland Sampy. We should be able to ask a general version later. You mean next year??? Who knows hopefully earlier. Here you are...

Oh, by the way the answer was not confirmed yet. So, the claim could be wrong.

A happy new year to everybody.

Labels:
circle,
Inscribed Circle,
proof,
semi-circle,
Tangent

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