Crux Mathematicorum Problem 5145
An isogonal configuration leading to concurrency
A problem proposed by Chikara Tsugawa and published as Crux Mathematicorum Problem 5145: an isogonal configuration whose associated lines are concurrent or parallel.
Problems
Problems
Original problems and selected solutions to existing problems. Each entry records its source and whether its solution is available.
Original Problems
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Selected Solutions
A Solution to BMO1 2025, Problem 4
A synthetic solution to BMO1 2025, Problem 4 using tangent–chord angles, cyclic symmetry, and power of a point.
A Solution to Crux Mathematicorum Problem 4941
Crux Mathematicorum Problem 4941, followed by an incircle-inversion proof using the medial triangle of the contact triangle.
A Solution to Crux Mathematicorum Problem 5021
Crux Mathematicorum Problem 5021, followed by a direct-similarity generalization proved with Pappus's theorem and a radical axis.
A Solution to Crux Mathematicorum Problem 5031
Crux Mathematicorum Problem 5031, followed by an incircle-inversion proof using contact-chord midpoints and a cyclic quadrilateral.
A Solution to Crux Mathematicorum Problem 5088
Crux Mathematicorum Problem 5088, followed by an angle-chasing proof through tangency and cyclic quadrilaterals.
A Solution to Crux Mathematicorum Problem 5098
Crux Mathematicorum Problem 5098, followed by a unit-circle complex proof that reduces two geometric conditions to the same algebraic equation.
A Solution to Crux Mathematicorum Problem 5109
Crux Mathematicorum Problem 5109, followed by a synthetic fixed-point argument and a projective generalization.
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