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QJEEM22Maa7ed: JEE Main 2022 Mathematics - Class 11 JEEM22Maa7ed Solution: Let be a chord of length 12 of the circle . If tangents drawn…

Let ABA B be a chord of length 12 of the circle (x−2)2+(y+1)2=1694(x-2)^{2}+(y+1)^{2}=\frac{169}{4} . If tangents drawn to the circle at points AA and BB intersect at the point PP , then five times the distance of point PP from chord ABA B is equal to __________.

Step-by-Step Verified Solution

Here AM=BM=6A M=B M=6

OM=(132)2−62=52O M=\sqrt{\left(\frac{13}{2}\right)^{2}-6^{2}}=\frac{5}{2}

JEE Main 2022 (Online) 29th July Evening Shift Mathematics - Circle Question 47 English Explanation

sin⁡θ=1213\sin \theta=\frac{12}{13}

In △PAO\triangle P A O :

amp;POOA=sec⁡θamp;PO=132⋅135=16910amp;∴PM=16910−52=14410=725amp;∴5PM=72.\begin{aligned}&\frac{P O}{O A}=\sec \theta \\\\&P O=\frac{13}{2} \cdot \frac{13}{5}=\frac{169}{10} \\\\&\therefore P M=\frac{169}{10}-\frac{5}{2}=\frac{144}{10}=\frac{72}{5} \\\\&\therefore 5 P M=72 .\end{aligned}

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