Starting from segments of lengths 1 and 7, a student used straightedge and compass ONLY to construct the following. [br][br]The student's strategy was to start with the segment of length 1 (AD=1) and then[br]construct a line through points A and D[br]copy the segment of length 7 so that DB=7[br]construct the perpendicular bisector of segment AB and let F denote the midpoint of segment AB[br]construct a semicircle with center F and radius 4[br]construct a perpendicular through D to segment AB and call its intersection with the semicircle C[br]connect the points A, B and C to form a triangle with angle C inscribed in the semicircle[br][br]What is the EXACT length of the segment with endpoints C and D? How do you know? (You must prove it!)