🔴Think You're Good at Geometry? Find the Radii Ratio | Advanced Geometry Challenge

Can you find the ratio of the radii of the two circles using only geometry? In this Advanced Geometry challenge, we construct an isosceles triangle OPA and divide it into two congruent right triangles using the radius of the smaller circle. We then express the side lengths of the right triangle in terms of r (the radius of the small circle) and R (the radius of the semicircle). Using the Pythagorean Theorem, we derive an equation relating r and R, leading to the exact radii ratio. This elegant proof combines circle geometry, right triangles, and algebra into a beautiful Olympiad-style solution. If you enjoy elegant geometry problems and mathematical proofs, like, subscribe, and share for more challenging math videos every week! Watch more ADVANCED videos here:    • ADVANCED MATH   Watch more CIRCLE GEOMETRY videos here:    • Circle Geometry   #AdvancedGeometry #CircleGeometry #Semicircle #Radius #RadiiRatio #PythagoreanTheorem #IsoscelesTriangle #RightTriangle #GeometryChallenge #MathChallenge #OlympiadMath #UKMT #ProblemSolving #Mathematics #MathTutorial #LearnMath #STEM #EuclideanGeometry #MathSpark