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If the radius of the circle touching the pair of lines `7x^(2) - 18 xy +7y^(2) = 0` and the circle `x^(2) +y^(2) - 8x - 8y = 0`, and contained in the given circle is equal to k, then `k^(2)` is equal to
A. 10
B. 9
C. 8
D. 7

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Correct Answer - C
image
`tan theta = |(2sqrt(h^(2)-ab))/(a+b)| =(4sqrt(2))/(7)`
`:. tan. (theta)/(2) = (1)/(2sqrt(2))`
`:. sin .(theta)/(2) = (1)/(3) = (sqrt(2)(8-alpha))/(sqrt(2)alpha)`
`:. alpha = 6`
Hence, equation of circle is `(x-6)^(2) +(y-6)^(2) = 8`.

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