No, no annoying philosophical stand here.

Just pure simple layyziness.

Note, the statement should hold in 3-D as well. Don't you agree?

And YES, "plane" is misspelled !

Why?

No, no annoying philosophical stand here.

Just pure simple layyziness.

No, no annoying philosophical stand here.

Just pure simple layyziness.

Labels:
Capitalism sucks,
Communism aint no better,
Orthogonal,
Poligon,
proof

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Labels:
Circle inside Square,
Pythagoras,
Square

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Labels:
Bisector,
chords,
circle,
General Case,
Law of Sines,
proof,
Solutions,
Trigonometry

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Labels:
Capitalism sucks,
Center of Gravity,
Parallel Lines,
Poligon

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We have been delaying this for a while, but **Ajit** and **Vihaan** have already solved it. So there is no point of keeping it a secret :)

Note that this may be a general case for Foxes: 296, 297, and 298. It is also related to Fox 301.

Note that this may be a general case for Foxes: 296, 297, and 298. It is also related to Fox 301.

Labels:
Bisector,
chords,
circle,
General Case,
proof,
Trigonometry

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Three distinct solutions were found for Fox 160.

The solution commented out by Julian deserves to be presented here. We often had questions inspired from the "things" we observe around us. Julian's solution is the other way. It uses a very casual observation from real-life for the Now imagine looking through the tube from one end to the other. You see two squares: a large square at the near end, and a smaller square at the far end. By subtly changing the direction the tube is pointing, the far square may move off centre so that the construction looks like the problem diagram. This will not alter the fact that the four lines meet at a single point. QED!

Analytic Geometry by Bob Ryden:

Observe that proving DH implies CG as well (due to rotation). Neat!

**Similarity of Triangles by Giannno:**

Labels:
Analytic Geometry,
proof,
similarity of triangles,
Solutions,
Square,
Square inside a square,
The truth is out there

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Labels:
Analytic Geometry,
circle,
Haiku,
Pythagoras,
Quadratics,
Solutions,
Square,
Trigonometry,
Uniqueness

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Labels:
Pythagoras,
simple proofs,
Square,
Square inside a square

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Labels:
Bisector,
chords,
circle,
General Case,
proof

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By definition OB=x+1 => OBH is an isosceles triangle (1).

Also known that, m(BHO)=90 degrees (2).

Also known that, m(BHO)=90 degrees (2).

Nope, aint gonna happen.

i.e. (1) and (2) can't happen at the same time.

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Let's mess around little bit more with this:

Labels:
Aint gonna happen,
Bisector,
chords,
circle

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Among similar ones, Bleaug finds a contradiction for Fox 296:Take an arbitrary AOC triangle such that OC=3OA. Build B as intersection of triangle's circumscribed circle and AOC internal bisector. B is such that ABC is isoceles, i.e. AB=BC. Symmetry in OABI implies AB=BI, hence IBC is isoceles. Orthogonal projection of B on OC coincides with H such that IH= HC=OA. OHB is rectangle, therefore

OB^2 = (2OA)^2 + BH^2 => OB > 2OA iff angle(AOC) > 0.

Strictly speaking, if angle(AOC)=0 there is a solution if we admit that a straight line is a circle with center at infinity (e.g. in projective plane).

__And Giannno solves too__:

OB^2 = (2OA)^2 + BH^2 => OB > 2OA iff angle(AOC) > 0.

Strictly speaking, if angle(AOC)=0 there is a solution if we admit that a straight line is a circle with center at infinity (e.g. in projective plane).

Labels:
Aint gonna happen,
Bisector,
chords,
circle,
Ptolemy,
similarity of triangles,
Solutions

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