Mathematics Question and Solution
a = atan(6/12)
a = 26.56505117708°
a = Angle BAE.
b = 45-26.56505117708
b = 18.43494882292°
b = Angle CAE.
d = ½√(2*12²)
d = 6√(2) cm.
d = half AC = radius of the circle.
Let the centre of the circle be O.
e = 180-2(18.43494882292)
e = 143.13010235416°
e = Angle AOF.
f² = 2*(6√(2))²-2*(6√(2))²cos143.13010235416
f = 16.099689438 cm.
f = AF.
g = 90-18.43494882292
g = 71.56505117708°
g = Angle AFN.
h = 180-71.56505117708-26.56505117708
h = 81.86989764584°
h = Angle ANF.
(16.099689438/sin81.86989764584) = (i/sin26.56505117708)
i = 7.27309832078 cm.
i = FN = NF.
j = 180-71.56505117708
j = 108.43494882292°
j = Angle AFM.
k = 180-108.43494882292-18.43494882292
k = 53.13010235416°
k = Angle AMF.
(16.099689438/sin53.13010235416) = (l/sin18.43494882292)
l = 6.36396103068 cm.
l = FM = MF.
It implies;
Length MF ÷ Length NF is;
6.36396103068÷7.27309832078
= 0.875
= 875/1000
= 35/40
= 7/8
