Online Geometry: Areas, Theorems and Problems - Page 5

Proposed Problem 139. Triangle Area, Orthic Triangle, Semiperimeter, Circumradius.

Right Triangles, Formulas and Facts
Pythagorean theorem, Similarity, Geometric mean, hypotenuse, catheti (legs), semiperimeter, altitude, median, similar shapes areas, centers, orthocenter, incenter, centroid, circumcenter, radius, inradius, circumradius, exradius, circles, incircle, circumcircle, excircle.

Pythagorean Theorem, 47th Proposition of Euclid's Book I, Video.

Heron's Formula.
Key facts and a purely geometric step-by-step proof.
 

Heron's Formula with medians 

Kurschak's Tile and Theorem. Jozsef Kurschak (Hungary, 1864-1933) An elegant and a purely geometric way of finding the area of a regular dodecagon.
 

Archimedes' Book of Lemmas. Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve these 15 high school level problems and lift up your geometry skills.
 
Proposition 4 Arbelos.

Archimedes Proposition 7. Circles and Squares.

Proposition 14 area of the Salinon.

Brahmagupta's Formula  Area of a cyclic quadrilateral.

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