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.

Geometry Problem 683: Nagel Point.
Triangle, Excircles, Tangency points, Concurrent lines, Semi-perimeter, Ceva theorem.

Geometry Problem 684: Outer Nagel Point.
Triangle, Excircles, Incircle Tangency points, Concurrent lines, Semi-perimeter, Ceva theorem.

Geometry Problem 685
Isosceles Triangle, 100-40-40 Degrees, Angles, Congruence.

Geometry Problem 686.
Triangle, Three Excircles, Tangency points, Tangent lines, Semi-perimeter, Congruence.

Geometry Problem 687.
Triangle, Three Excircles, Tangency points, Concurrent Lines.

Geometry Problem 688.
Triangle, Angles, 10, 20, 30, 40, 60 Degrees, Measure, Mind Map, Polya.

Geometry Problem 689.
Triangle, Three Excircles, Tangency points, Tangent lines, Concurrent Lines, Mind Map.

Problem 690: Distance between the Incenter and the Centroid of a Triangle.
Formula in terms of the sides a,b,c.