Gogeometry Problem 406

 dans Euclide Geometry Problem / Géométrie Euclidienne  étiqueté 15 degrees / Congruence / Midpoints / Right Triangle par Harvey Littleman

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From Gogeometry

Using

• Inscribed angles in a circle
• Equilateral triangle
• Concyclic points

∠BAD= π/2 => B, A and D are concyclic, circle with center F middle of BD
=> FB=FA=FD and ∠BAF=15°
In the same way, GC=GA=GE and ∠CAG=15°
=>∠FAG=90-15-15=60°
ΔFAG is isosceles in A (AF=AG) and ∠FAG=60° => ΔFAG is equilateral

Therefore x=FG=BD/2=CE/2=1

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