Gergonne Points, Triangle Centers. Elearning, College Geometry Online.

College Geometry Online, eLearning

Triangle Centers & Concurrency The Gergonne Point: A Symphony of Concurrency and Tangency Deep within the triangle’s heart lies the Gergonne Point, a masterpiece of synthetic Euclidean geometry. This point emerges where the lines connecting vertices to the contact points of the incircle meet in perfect unison. Explore the theorems, proofs, and challenges that define this elegant intersection of symmetry and proportion.

	Gergonne Point Theorem. Concurrency. Interactive proof with animation. HTML5 Animation for Tablets (iPad, Nexus) Adobe Flash Animation Key concept: Ceva's Theorem.
	Typography of Gergonne Point.
	Geometry Problem 1616: Incenter and Segment Ratios in a Contact Triangle
$Geometry Problem 1024$	Geometry Problem 1024. Contact, Gergonne Triangle, Point on an arc of Incircle, Perpendicular, Distances.
$Geometry Problem 1023$	Geometry Problem 1023. Triangle, Contact, Gergonne, Product of three distances.
	Geometry Problem 821. Adams Circle.
	Geometry Problem 689. Triangle, Three Excircles, Tangency points, Tangent lines, Concurrent Lines, Mind Map.
	Geometry Problem 687. Triangle, Three Excircles, Tangency points, Concurrent Lines.
	Geometry Problem 681: Gergonne Point. Triangle, Incircle, Tangency points, Concurrent lines, Semiperimeter, Ceva theorem.
	Geometry Problem 682: Gergonne External Point. Triangle, Excircle, Tangency points, Concurrent lines, Semiperimeter, Ceva theorem.
	Semiperimeter and excircles of a triangle.
	Semiperimeter and incircle of a triangle.
	Semiperimeter, incircle and excircles of a triangle.

The Gergonne Point: A Symphony of Concurrency and Tangency