... sides of thepolygon with the circle to l is independent of the position of the line l.Problem 125 [Loney]If 2φ1, 2φ2, 2φ3are the angles subtended by the circle es cribed to the side ... circles (r1does not touchthe side DC, r2the side DA, r3the side AB and r4the side BC). Provethat|AB|r1+|CD|r3=|BC|r2+|AD|r4Problem 145The sides of a square is equal to a ... inthe plane to the sides of a triangle takes on the least value for such a pointinside the triangle whose distances to the corresponding sides are propor-tional to these sides. Prove also that...