MathDB
square interior to a square, 5 equal incircles, 4 right triangles

Source: 2018 Portugal p2

October 11, 2020
geometryincircleSquaressquare

Problem Statement

In the figure, [ABCD][ABCD] is a square of side 11. The points E,F,GE, F, G and HH are such that [AFB],[BGC],[CHD][AFB], [BGC], [CHD] and [DEA][DEA] are right-angled triangles. Knowing that the circles inscribed in each of these triangles and the circle inscribed in the square [EFGH][EFGH] has all the same radius, what is the measure of the radius of the circles? https://1.bp.blogspot.com/-l37AEXa7_-c/X4KaJwe6HQI/AAAAAAAAMk4/14wvIipf26cRge_GqKSRwH32bp291vX4QCLcBGAsYHQ/s0/2018%2Bportugal%2Bp2.png