Geometry puzzle (17) Problem In picture below AD = DC LABC = 45 deg. Question: find angle x. Solution Draw circle with center D and radius AD. E is intersection of AB with circle. Draw line CE. Draw line DE. LAEC = 90....... {spans circle arc of 180 deg.). LBCE = 45 .....so.. BE = CE. LAED = LDAE = 2x. LCDE = 2x + 2x = 4x......{exterior angle of triangle AED}. LAED = 2x = x + LBDE.....LBDE = x.....DE = BE. Conclusion: CD = DE = EC. Triangle CDE equilateral. LCDE = 4x = 60. x = 15 deg.