Math.......Properties of Circles

圖片參考：http://x63.xanga.com/baed275132233105171767/m74350588.jpg

AC = BC =15cm and AB = 6cm
(a)
AN=BN=3 cm
CN
= √(15^2-3^2)
=√(225-9)
=14.7 cm
(b)
AB^2=AC^2+BC^2-2(AC)(BC) cos(ACB)
36=225+225-450(cos(ACB))
cos(ACB)=0.92
angle ACB=23.074
angle ACN=angle BCN=11.537
angle OAC=angle ACN=11.537
angle AOC=156.926
AC^2=OA^2+OC^2-2(OA)(OC)cos(AOC)
225=2OA^2-2OA^2(cos156.926)
225=3.84OA^2
OA=7.655 cm
the radius of the circle is 7.655 cm

a)AN=BN=0.5AB=3cm (lines from centre perpendicular to chord bisect chord)
By Pyth. Theorem,
CN^2 = AC^2 - AN^2 = 15^2 - 3^2
CN^2=216
CN=6(root 6)cm

b)radius=0.5CN=3(root6)cm

2007-02-06 23:24:02 補充：
b)x=angle AOC, y=angleACNsiny=3/15, y=11.53 degreex=180-2y=156.93 degreeBy sine formula,r/siny=15/sinx15r/3=15/0.392r = 7.655cm