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

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How to calculate the area of this Blue Triangle? This video explains the solution by two different methods.

[GoogleAccount-pict]

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).

[rabotaakk-nwnm]

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.

[marcusdrevor]

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