The equation of a circle is S 1 ≡ x 2 + y 2 = 1 . The orthogonal tangents to S 1 meet at another circle S 2 and the orthogonal tangents to S 2 meet at the third circle S 3 . Then

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The equation of a circle is S 1 ​ ≡ x 2 + y 2 = 1 . The orthogonal tangents to S 1 ​ meet at another circle S 2 ​ and the orthogonal tangents to S 2 ​ meet at the third circle S 3 ​ . Then

TestHub · Accepted Answer

Orthogonal tangents to a circle meet at the director circle $∴ S_{2} \equiv x^{2} + y^{2} = 2.1 \Rightarrow S_{2} \equiv x^{2} + y^{2} = 2$

Also, $S_{3} \equiv x^{2} + y^{2} = 4$

Ratio of radius of $S_{2}$ and $S_{3} = 2 : 2 = 1 : 2$

Also, the three circles are concentric

Mathematics - Circle Question with Solution | TestHub

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