The Golden Section in the Inscribed Square of an Isosceles Right Triangle

Abstract. We prove the occurrence of the golden section with the inscribed square of an isosceles right triangle on its hypotenuse and its circumcircle. Given a right isosceles triangle ABC and its circumcircle, inscribed a square DEFG with a side FG along the hypotenuse AB. If the side DE is extended to intersect the circumcircle at P, then E divides DP in the golden ratio (see Figure 1). This is reminiscent of the golden section by Odom’s construction [2]; see also [1]