How to find the area of the blue triangle? | Solution by two methods | Geogebra Math Problem

[@mahdimousavi4536]

Good❤

[@LearnMathwithZain]

Thank you 🌷🙏❤️

[@mrmrstanvinforever2669]

Method 2 gossebumps😊

[@LearnMathwithZain]

Thank you for your comments. 🌹❤️

[@GoogleAccount-pi9ct]

This is actually a pretty cool problem. Here's my solution: Notice that 2 vertices are given on a diagnal of a square, and that the locus of the 3rd point is the possible circle centers, which is a line paralell to the diagnol at one of the vertices, and the height between any 2 paralell lines is constant so just drop an altitude, use Pythagorean theorem, and get 18. Suggestion: please mix in some harder problems like AIME final 5 or early end USAMO problems (or anything along that level in other nations).

[@LearnMathwithZain]

Thank you for your comment and suggestion. I will work on it. ❤️

[@marcusdrevor5072]

I could grasp "d" is 6 into root 2 intuitionally but can you please proof it?

[@rabotaakk-nw9nm]

Задача с "недостатком данных" решается методом "крайностей": принимаем не заданный радиус окружности равным 0. Тогда вершина треугольника совпадёт с вершиной квадрата и синий треугольник становится прямоугольным, с катетами 6 и 6. Его площадь=6×6/2=18.