Let h be a semicircle with diameter AB. Let P be an arbitrary point inside the diameter AB. The perpendicular through P on AB intersects h at point C. The line PC divides the semicircular area into two parts. A circle will be inscribed in each of them that touches AB,PC and h. The points of contact of the two circles with AB are denoted by D and E, where D lies between A and P. Prove that the size of the angle DCE does not depend on the choice of P.(Walther Janous) geometrymixtilinearfixedfixed anglesemicircle