Question

如图，PAB,PCD是圆O的两条割线，AB是圆O的直径。

如图，PAB,PCD是圆O的两条割线，AB是圆O的直径。（1）如图甲，若PA=8,PC=10,CD=6.求SIN角APC的值；(2)SIN角BOD
只要回答(2),且只要答案

Answer 1

4√3/7

Answer 2

r²-9+13²=(8+r)²
r=6
sinAPC=3√3/14

BD²=PD²+PB²-2PD×PBcosAPC=256+400-640×13/14=656-4160/7
BD²=OD²+OB²-2OD×OBcosBOD
cosBOD=1/7
sinBOD=4√3/7

Answer 3

解：(1)PA*PB=PC*PD=>PB=PC*PD/PA=20 =>AB=16 =>OA=OB=OC=6
过O做CD的垂线垂足为M，显然OM=sqrt(OD^2-DM^2)=3sqrt(3);
SIN角APC=OM/OP=3sqrt(3)/14
(2)过D做AB的垂线垂足为N，显然DN/PD=SIN角APC
=>DN=SIN角APC*PD=24sqrt(3)/7
SIN角BOD=DN/OD=24sqrt(3)/7/6=4sqrt(3)/7