Maths 圓的基本性質 20點

14a) ∵BA=AC(given)
∴ arc BA = arc AC =4cm (equal chords, equal arcs)
Arc BC= arc BA + arc AC
Arc BC=4x2=8cm


14b) angle BOC =146 (given)
∵BA=AC(given)
∴x=y (equal chords, equal arcs)
x=y= 146/2
x=y=74度

2013-09-21 00:32:23 補充：
30a) arc BCF : arc AFC =5:6
∴angle BAF: angle CBA=5 :6
75度 :angle CBA = 5:6
75/ angle ABC= 5/6
Angle ABC = 90度

2013-09-21 00:49:57 補充：
b)angle FCB=180- 70= 110度(opp. Angles, cyclic chord)
angle AFC= 180-90= 90度(opp. Angles, cyclic chord)

angle EFC= 180 - angle AFC(90度) =90度 (adj angles on st line)
angle DCF= 180- angle FCB= 70度

x=180-angle EFC =90度
y= 180- DCF= 110度

^_^ 你犯了一個策略上的錯誤～

14.
(a)
arc BC = arc BA + arc AC = arc BA + arc BA = 8 cm
(because equal chords, equal arcs)

(b)
x = y (because equal chords, equal angles)
x + y = 146°
2x = 146°
x = y = 73°

2013-09-20 22:22:53 補充：
27.
(a)
留意 a + d = ∠DGC = ∠FGB
同時 e + c = ∠EFA = ∠GFB
看 △FGB, (a+d)+(e+c)+b = 180°

(b)
d:e:a:b:c = 1:2:1:3:2 (arcs prop. to angles at circum)
Let a, b, c, d, e be k, 3k, 2k, k, 2k, respectively.
By (a), k+3k+2k+k+2k = 9k = 180°
k = 20°
e = 2k = 40°