Enigma

Enigmes & Problèmes scientifiques

Géométrie Euclidienne

From Gogeometry Using : Additional points Similar triangles •ΔABC is isosceles and right in B => BA=BC and ∠BAC=∠BCA=Π/4 • Define G in AC such as AB=AG => ΔBAG is isosceles in A •Define H intersection of AD and BG •∠BAH=∠GAH=Π/4/2=Π/8 and HB=HG and ∠AHB=∠AHG=Π/2 •and ∠ABH=∠AGH and ∠ABH+ ∠BAH […]

Gogeometry Problem 975

dans Euclide Geometry Problem / Géométrie Euclidienne étiqueté 45 Degrees / Angle Bisector / Hypotenuse / Isosceles Right Triangle par Harvey Littleman

From Gogeometry Using : Additional points Tangents to a circle •(1) AF=ra=r+EB+BF=r+a2 •(2) AG=ra=r+DC+CG=r+a1 •(1-2) a1=a2 •(1+2) ra=r+a1=r+a2 => a1=a2=ra-r •Define X as the intersection of BC and circle ra •Define Y as the intersection of BC and circle r •CD and CY tangents to circle r => CD=CY •BE […]

Gogeometry Problem 207

dans Euclide Geometry Problem / Géométrie Euclidienne étiqueté Exradius relative to the hypotenuse par Harvey Littleman

From Gogeometry Using : Isometric transformation Inscribed angles in a circle Equilateral triangle Tangents to a circle Define R radius of circle O and r radius of circle Q By construction and symmetry A, O, Q, D are collinear DE=DF, AE=AF AD angle bisector of ∠BAC D symmetric of A […]

Gogeometry Problem 1362

dans Euclide Geometry Problem / Géométrie Euclidienne étiqueté Equilateral Triangle Inscribed in a Circle / Lunula / Ratio of Areas / Sketch / Tangent par Harvey Littleman

Using : Additional points Pythagoras Similar triangles Thales theorem Tangents to a circle

Problem H003

dans Euclide Geometry Problem / Géométrie Euclidienne étiqueté circle par Harvey Littleman