
Geometry problem below was found in Facebook group "PI love math".
AD=DB
Question: prove that x=22.5
The proof
step 1:
draw perpendicular bisector of AB. E is intersection with BC.
draw AE.
LDAE=LDBE=x
LAEC=x+x=2x.....(exterior angle of ΔABE)
LCAE=2x
Conclusion: AC=EC
step 2:
draw perpendicular bisector of AE, F is intersection with extended DE.
draw FA.
LAEF=90x
LEFC=LAFC=x
LDAF=902x
step 3:
observe ΔADF
FC is bisector of interior angle F.
DC is bisector of exterior angle D.
conclusion: AC is bisector of exterior angle A.
step 4:
observe angles at point A.
3x + 3x + 902x = 180
4x=90
x=22.5^{0}

