由 ---- 於 星期四 六月 19, 2003 12:52 pm
angle AEB=angleADB=90
A,B,D,E are concyclic (converse of angle in same seg.)
angle ADC=angle AFC=90
A,D,C,F are concyclic (opp. angles supp.)
angle ABC=angle AEF (angle in same seg.)
angle ACB=angle AFE (angle in same seg.)
Angle BAC=180-angle ABC-angleACB(angle sum of triangle)
=180-angle AEF-angleAFE
=angle EAF
Therefore ABC~AEF (AAA)
angle ABM = angle AEN (corr. angle, ~tri.)
AB/AE = BC/EF =BM/EN (corr. sides, ~tri.)
Therefore ABM~AEN (ratio of two sides, included angle)
angle AMB = angle ANE (corr. angles, ~tri.)
Therefore A,D,M,N are concyclic (converse of angle in same seg.)
Angle ANM + angle ADC = 180 (opp. angle, cyclic quad.)
Angle ANM = 90