F.4 Maths about circle

圖片參考：http://i240.photobucket.com/albums/ff164/walkinginthesang/ebb84548.jpg?t=1193662519

First using Pythagoras' Theorem, list two relationships
BC^2=AB^2+AC^2
AB^2=AP^2+BP^2
That is
BC^2=AB^2+100...(1)
AB^2=36+BP^2...(2)
sub (2) into (1)
BC^2=36+BP^2+100
BC^2=BP^2+136
BC^2=(BC-CP)^2+136
BC^2=(BC-8)^2+136
BC^2=BC^2-16BC+200
16BC=200
BC=12.5
The radius of circle
=BC/2
=6.25 cm

2007-10-29 23:00:57 補充：
AP*AP = BP*PC 這條定理是對的﹐但教科書一般不載﹐長題目要用的話應該要先證一次。那麼工作量便和上面差不多。當然記住對做mc有用。

AP*AP = BP*PC (property of circle)
6*6 = BP*8
therefore BP = 4.5
Dia. = BP +PC = 4.5+8 = 12.5
therefore radius = 12.5/2 = 6.25 cm