Let A B be a chord of length 12 of circle (x-2)^{2}+(y+1)^{2}=frac{169}{4} If tangents drawn to circ

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10-1.Circle and System of Circles

hard

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$.......$

A

$71$

B

$73$

C

$72$

D

$74$

(JEE MAIN-2022)

Solution

$\cos \theta=\frac{6}{\frac{13}{2}}=\frac{12}{13}$

$\sin \theta=\frac{5}{13}$

$PM = AM \cot \theta$

$PM =6\left(\frac{12}{5}\right) \therefore 5( PM )=72$

Standard 11

Mathematics

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