If `A(0, 0), B(1, 0) and C(1/2,sqrt(3)/2)` then the centre of the circle for which the lines `AB,BC, CA` are tangents is

If O=(0,0),A=(1,0) and B=(1/2,(sqrt(3))/2) then centre of circle for which the lines OA, OB and AB are tangents is

If O=(0,0), A=(1,0) and B=(1//2, sqrt3//2) then the centre of the circle for which the lines OA, Ab and BO are the tangents, is

if P=(0,0),Q=(1,0) and R=((1)/(2),(sqrt(3))/(2)), then the centre of the circle for which the lines PO,QR and RP are tangents is

If P(0,0), Q(1,0) and R (1/2,sqrt3/2) are three given points, then the centre of the circle foe which the lines PQ, QR and RP are the tangents is

If P(0,0,)Q(1,0)andR((1)/(2),(sqrt3)/(2)) are three given points, then the centre of the circle for which the lines PQ,QR and RP are the tangents is

If A(2, -1), B(3, 1), C(1, -2) then the radical centre of the circles with AB, BC, CA as diameters is

If A(-2,1),B(3,2),C(-1,-2) then the radical centre of the circles with AB,BC ,CA as a diameter is

If A, B, C, be the centres of three co-axial circles and t_(1),t_(2),t_(3) be the lengths of the tangents of them any piont, prove that bar(BC).t_(1)^(2)+bar(CA).t_(2)^(2)+bar(AB).t_(3)^(2)=0

If A, B, C, be the centres of three co-axial circles and t_(1),t_(2),t_(3) be the lengths of the tangents of them any piont, prove that bar(BC).t_(1)^(2)+bar(CA).t_(2)^(2)+bar(AB).t_(3)^(2)=0