Let ABC be a triangle, all of whose angles are greater than 45∘ and smaller than 90∘.
(a) Prove that one can fit three squares inside ABC in such a way that: (i) the three squares are equal (ii) the three squares have common vertex K inside the triangle (iii) any two squares have no common point but K (iv) each square has two opposite vertices onthe boundary of ABC, while all the other points of the square are inside ABC.
(b) Let P be the center of the square which has AB as a side and is outside ABC. Let rC be the line symmetric to CK with respect to the bisector of ∠BCA. Prove that P lies on rC. geometry proposedgeometry