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