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[" 23.Through a given point "P(5,2)" ,se...

[" 23.Through a given point "P(5,2)" ,secants are drawn to cut the circle "x^(2)+y^(2)=25" at points "],[A_(1)(B_(1)),A_(2)(B_(2)),A_(3)(B_(3)),A_(4)(B_(4))" and "A_(5)(B_(5))" such that "PA_(1)+PB_(1)=5,PA_(2)+PB_(2)=6],[PA_(3)+PB_(3)=7,PA_(4)+PB_(4)=8" and "PA_(5)+PB_(5)=9." Find the value of "sum_(i=1)^(5)PA_(i)^(2)+sum_(i=1)^(5)PB_(i)^(2)]

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Delta_(1)=det[[a_(1)+pb_(1),b_(1)+qc_(1),c_(1)+ra_(1)a_(2)+pb_(2),b_(1)+qc_(2),c_(2)+ra_(2)a_(3)+pb_(3),b_(3)+qc_(3),c_(3)+ra_(3)]]