1.

If the polar of a point on the circle x^(2) + y^(2) = p^(2) with respect to the circle x^(2) + y^(2) = q^(2) touches the circle x^(2) + y^(2) = r^(2) then p,q r are in

Answer»

AP
GP
HP
AGP

Solution :Given CIRCLES are `S_(1) = x^(2) + y^(2) - p^(2) = 0, S_(2) = x^(2) + y^(2) - Q^(2) =0`
and `S_(3) = x^(2) + y^(2) - R^(2) = 0`
Let p `(x_(1), y_(1))` be a point on `S_(1) - 0` then `S_(1) = x_(1)^(2) + y_(1)^(2) - p^(2)`
EQUATION of polar of p w.r.t `s_(2) = 0` is `x x_(1) + y y_(1) - q^(2) - 0`
Equation (1) touches the circle S = 0 then
`r = (|0 + 0 - q^(2)|)/(sqrt(x_(1)^(2) + y_(1)^(2)))`
`implies q^(2) = r sqrt(x_(1)^(2) + y_(1)^(2))`
`implies q^(2) = r sqrt(P^(z))`
`implies q^(2) = pr`
`:.` p.q and r are in G.P


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