A Solution to Crux Mathematicorum Problem 5031
A concise incircle-inversion proof using contact-chord midpoints and a cyclic quadrilateral, presented without reproducing the original problem statement.
Topic
Triangle geometry
8 entries in this archive currently use this topic.
A Solution to Crux Mathematicorum Problem 5088
A concise angle-chasing proof through tangency and cyclic quadrilaterals, presented without reproducing the original problem statement.
A Solution to Crux Mathematicorum Problem 5098
A unit-circle complex proof that reduces two geometric conditions to the same algebraic equation, presented without reproducing the original problem statement.
A Solution to Crux Mathematicorum Problem 5109
A synthetic fixed-point argument and a projective generalization, presented without reproducing the original problem statement.
Incircle Inversion for Problem 5031
The incircle, its contact points, and the auxiliary intersections used in the inversion solution to Crux Mathematicorum Problem 5031.
Tangent Circle in a Parallelogram
The tangent circle, perpendicular feet, and cyclic configurations used in the solution to Crux Mathematicorum Problem 5088.
Cyclic Orthocenter Configuration
A cyclic quadrilateral, two altitude feet, and an orthocenter in the configuration used for the solution to Crux Mathematicorum Problem 5098.
Auxiliary Rectangle for a Fixed-Point Solution
The rectangle, perpendicular feet, and two intersections used in the solution to Crux Mathematicorum Problem 5109.