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  4. Let A B be a chord of length 12 of the circle (x-2)2+(y+1)2=(169/4) If tangents drawn to the circle at points A and B intersect at the point P, then five times the distance of point P from chord AB is equal to

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Q. Let $A B$ be a chord of length 12 of the circle $(x-2)^2+(y+1)^2=\frac{169}{4}$ If tangents drawn to the circle at points $A$ and $B$ intersect at the point $P$, then five times the distance of point $P$ from chord $AB$ is equal to

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Solution:

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$ \cos \theta=\frac{6}{\frac{13}{2}}=\frac{12}{13}$
$\sin \theta=\frac{5}{13} $
$ PM = AM \cot \theta $
$ PM =6\left(\frac{12}{5}\right) $
$\therefore 5( PM )=72$