Group

Triangle and Circle Geometry

This group gathers theorems about triangles, circles, and the points, lines, and circles constructed from them, the largest and most classical family of results in plane geometry. It covers the special centers and circles associated with a triangle, including the nine-point circle, the Euler line theorems, and Morley's trisector theorem, the concurrence and collinearity theorems of Ceva, Menelaus, and Miquel, circle theorems such as Ptolemy's, the inscribed angle theorem, and the power of a point, and further classical identities relating a triangle's or cyclic polygon's sides, angles, and area.

Facts

Comparison

Era Of Emergence

300 BCE 1

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All Triangle and Circle Geometry

Triangle and Circle Geometry

40 entries

Triangle and Circle Geometry

40 entries

Branch

Topic Area

Proved

Proved By

Statement Form

1. Wikipedia: Geometry

Wikimedia FoundationHistory section

Quote, History section

Around 300 BC, geometry was revolutionized by Euclid, whose Elements, widely considered the most successful and influential textbook of all time, introduced mathematical rigor through the axiomatic method.

All Triangle and Circle Geometry

Angle Bisector Theorem

Apollonius's Theorem

Brahmagupta Theorem

Bretschneider's Formula

Butterfly Theorem

Carnot's Theorem

Casey's Theorem

Ceva's Theorem

Clifford's Circle Theorems

Conway Circle Theorem

Descartes Circle Theorem

Equal Incircles Theorem

Erdos-Mordell Inequality

Feuerbach's Theorem

Five Circles Theorem

Geometric Mean Theorem

Heron's Formula

Inscribed Angle Theorem

Intersecting Chords Theorem

Intersecting Secants Theorem

Japanese Theorem for Cyclic Polygons

Japanese Theorem for Cyclic Quadrilaterals

Lester's Theorem

Menelaus's Theorem

Miquel's Theorem

Monge's Theorem

Morley's Trisector Theorem

Napoleon's Theorem

Nine-Point Circle Theorem

Petersen-Morley Theorem

Pompeiu's Theorem

Ptolemy's Theorem

Routh's Theorem

Simson Line Theorem

Six Circles Theorem

Steiner-Lehmus Theorem

Stewart's Theorem

Tangent-Secant Theorem

Thales' Theorem

Van Schooten's Theorem