This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2025 India STEMS Category B, 5
Tags: rhombus , homothety , arc-midpoint , Nine Point Circle
Let $ABC$ be an acute scalene triangle. Let $D, E$ be points on segments $AB, AC$ respectively, such that $BD=CE$. Prove that the nine-point centers of $ADE$, $ACD$, $ABC$, $AEB$ form a rhombus. [i]Proposed by Malay Mahajan and Siddharth Choppara[/i]

2025 India STEMS Category A, 5
Tags: rhombus , homothety , arc-midpoint , Nine Point Circle
Let $ABC$ be an acute scalene triangle. Let $D, E$ be points on segments $AB, AC$ respectively, such that $BD=CE$. Prove that the nine-point centers of $ADE$, $ACD$, $ABC$, $AEB$ form a rhombus. [i]Proposed by Malay Mahajan and Siddharth Choppara[/i]