A right triangle ABC is given. Point D is an orthographic view of point C on the hypotenuse AB. Points I and J are the centers of the circles inscribed in ADC and BDC triangles, respectively. Line g different from AB, is tangent to both circles, with the two circles being on the same straight side of g. The points P and Q are the points of intersection of the line g respectively with sides AC and BC. Prove that the CP IJQ pentagon can be inscribed in a circle.