圆X^2+Y^2-6X-8Y+20=0====>(X-3)²+(Y-4)²=(√5)²
∴设圆心M(3,4),连结OM,交PQ于N,OM=√(3²+4²)=5,PM=QM=√5
∴OP=√[5²-(√5)²]=2√5
∵Rt△OMP∽Rt△OPN
∴PN/OP=PM/OM===>PN=(2√5)(√5)/5=2
∴PQ=2PN=4