If the chord of contact of tangents from a po | vedclass

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(C) Let a point on the circle $x^2 + y^2 = r_1^2$ be $(r_1 \cos 	heta, r_1 \sin 	heta)$.The equation of the chord of contact of tangents from this p

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$G.P.$

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(C) Let a point on the circle $x^2 + y^2 = r_1^2$ be $(r_1 \cos 	heta, r_1 \sin 	heta)$.The equation of the chord of contact of tangents from this point to the circle $x^2 + y^2 = r_2^2$ is given by $x(r_1 \cos 	heta) + y(r_1 \sin 	heta) = r_2^2$.This chord touches the circle $x^2 + y^2 = r_3^2$. The perpendicular distance from the origin $(0, 0)$ to this line must be equal to the radius $r_3$.Using the formula for perpendicular distance $d = \frac{|ax_0 + by_0 + c|}{\sqrt{a^2 + b^2}}$,we get:$r_3 = \frac{|r_2^2|}{\sqrt{(r_1 \cos 	heta)^2 + (r_1 \sin 	heta)^2}}$$r_3 = \frac{r_2^2}{r_1 \sqrt{\cos^2 	heta + \sin^2 	heta}}$$r_3 = \frac{r_2^2}{r_1}$$r_2^2 = r_1 r_3$Since $r_2^2 = r_1 r_3$,the terms $r_1, r_2, r_3$ are in $G.P.$

Column-$I$	Column-$II$
$(a)$ Gymnosperms	$(p)$ Trimerous flowers
$(b)$ Monocots	$(q)$ Absence of flowers
$(c)$ Dicots	$(r)$ Primitive flowers
$(d)$ Pteridophytes	$(s)$ Tetramerous or pentamerous flowers

If the chord of contact of tangents from a point on the circle $x^2 + y^2 = r_1^2$ to the circle $x^2 + y^2 = r_2^2$ touches the circle $x^2 + y^2 = r_3^2$,then $r_1, r_2, r_3$ are in:

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