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From the variable point A on circle x^2+...

From the variable point `A` on circle `x^2+y^2=2a^2,` two tangents are drawn to the circle `x^2+y^2=a^2` which meet the curve at `Ba n dCdot` Find the locus of the circumcenter of ` A B Cdot`

Text Solution

Verified by Experts

The correct Answer is:
`x^(2)+y^(2)=(a^(2))/(2)`
Clearly, `x^(2)+y^(2)=2a^(2)` is director circle of the circle `x^(2)+y^(2)=a^(2)`.
Hence, in the diagram , ABOC is a square and circumcenter P(h,k) of `Delta ABC` is the midpoint of OA.
Hence,
`sqrt(h^(2)+k^(2))=(sqrt(2)a)/(2)`
or the locus is
`x^(2)+y^(2)=(a^(2))/(2)`
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