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

Question

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 A B is equal to _____.

TestHub · Accepted Answer

Plotting the diagram of given value we have,
Now given, radius $= \frac{\sqrt{169}}{\sqrt{4}} = \frac{13}{2}$
Now by diagram $M$ is the midpoint of $A B$ so, $A M = 6$
Now in $∆ A M P$ , $P M = 6 \cot θ$
And in $∆ O A M$
$\sin (90 ° - θ) = \frac{6}{\frac{13}{2}}$
$\Rightarrow \cos θ = \frac{12}{13}$
$P M = 6 \times \frac{12}{5} = \frac{72}{5}$
$\Rightarrow 5 P M = 72$

Mathematics - Circle Question with Solution | TestHub

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