Problem 331. Discovering the Relationship between Distances from a Point on the Inscribed Circle to Tangency Point and Vertices in a Square. Level: High School, College, SAT Prep. The figure shows a square ABCD with P on the inscribed circle O. If E, F, G, and H are the tangency points, prove that .    Thematic Poem: Unraveling the Mystery: The Relationship Between Points on an Inscribed Circle and Tangency Points in a Square Amidst the squares and angles of our minds,Lies a mystery waiting to be found,A hidden path that none yet unwinds,A puzzle yet to be unbound. Discovering the relationship between,Distances of a point on circle's arc,To tangency points and vertices seen,A revelation, a brand-new spark. The inscribed circle, a central guide,With its point in question, a starting place, We take a journey with eyes open wide,And unravel a puzzle with skill and grace. With each step forward, we find a clue,And piece by piece, the picture emerges clear,A new perspective that once was askew,Now seen with clarity, without a single tear. The distance to vertices, the tangency points,All speak to us in silent code,A language that our heart anoints,As we walk the path, on this quest we strode. The thrill of discovery, a journey worthwhile,A quest that feeds the mind and soul,The beauty of numbers, an endless pile,As we uncover mysteries, a story untold. In this journey, we find a new friend, A geometry that speaks to us in rhyme,A love for numbers, that never ends,And a journey that transcends time. Recent Additions