∠AOB=45°,OP= 4根號(hào)2,OQ=7
根據(jù)余弦定理：
PQ^2=OP^2+OQ^2-2OP*OQcos45°
=(4根號(hào)2)^2+7^2-2*4根號(hào)2*7*根號(hào)2/2=25
PQ=5
PD/DQ=2/3
PD/(PD+DQ)=2/(2+3)
PD/PQ=2/5
半徑PD=PQ*2/5=5*2/5=2
OP=4根號(hào)2,PD=2,QD=OQ=r,根據(jù)余弦定理：
PQ^2=OP^2+OQ^2-2OP*OQcos45°
如果外切：PQ=PD+QD=2+OQ
(PD+QD)^2=(4根號(hào)2)^2+OQ^2-2*4根號(hào)2*OQ*根號(hào)2/2
(2+OQ)^2=32-8OQ
OQ^2+12OQ-28=0
(OQ+14)(OQ-2)=0
OQ+14＞14
∴OQ=2
如果內(nèi)切：PQ=QD-PD=OQ-2
(QD-PD)^2=(4根號(hào)2)^2+OQ^2-2*4根號(hào)2*OQ*根號(hào)2/2
(OQ-2)^2=32-8OQ
(OQ+2)^2=32
(OQ+2+4根號(hào)2)(OQ+2-4根號(hào)2)=0
OQ+2+4根號(hào)2＞0
∴OQ+2-4根號(hào)2=0
∴OQ=4根號(hào)2-2