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

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 AB is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/5301d291122a7e3f1e50d75595f49be5-.png" /> cos θ=(6/(13)2)=(12/13) sin θ=(5/13) PM = AM cot θ PM =6((12/5)) ∴ 5( PM )=72

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 $A B$ is equal to

$cos θ = \frac{6}{\frac{13}{2}} = \frac{12}{13}$
$sin θ = \frac{5}{13}$
$PM = A M cot θ$
$PM = 6 (\frac{12}{5})$
$∴ 5 (PM) = 72$

Q. Let AB be a chord of length 12 of the circle (x−2)2+(y+1)2=4169​ 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

cosθ=213​6​=1312​ sinθ=135​ PM=AMcotθ PM=6(512​) ∴5(PM)=72

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 $A B$ is equal to

$cos θ = \frac{6}{\frac{13}{2}} = \frac{12}{13}$
$sin θ = \frac{5}{13}$
$PM = A M cot θ$
$PM = 6 (\frac{12}{5})$
$∴ 5 (PM) = 72$