AP EAPCET 19-Aug-2021 Shift 1 Paper

Let (x1,y1) be any point on the circle
x2+y2=r2
Then, x12+y12=r12 ...(i)
Equation of chord of contact of tangents from (x1,y1) to the circle x2+y2=r22 is
xx1+yy1=r22 ...(ii)
∵ Eq. (ii) touches the circle
x2+y2=r32
The length of perpendicular from centre (0,0) on Eq. (ii) is radius =r3
⇒

r22

√x12+y12

=r3
⇒

r22

√r12

=r3
⇒r22=r1r3
⇒r1,r2,r3 are in GP.