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  • Let be a chord of length 12 of the circle <img alt="\mathrm{(x-2)^{2}+(y+1)^{2}=\frac{169}{4}}" src="/latex-image/?%5Cmathrm%7B%2

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

Option: 1

72


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\begin{aligned} &\mathrm{\sin \theta=\frac{B E}{B C}=\frac{6}{\frac{13}{2}}=\frac{12}{13}}\\ &\text{Now }\mathrm{ \frac{B E}{\rho E}=\tan (90-\theta)}\\ &\mathrm{\Rightarrow \frac{6}{P E}=\cot \theta} \\ &\mathrm{\Rightarrow P E=6 \tan \theta=6 \cdot \frac{12}{5}=\frac{72}{5} }\\ &\mathrm{\Rightarrow 5 P E=72}\\ &\mathrm{Ans: 72} \end{aligned}

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