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  • There are exactly two chords of the circle that passes through (1,

There are exactly two chords of the circle \mathrm{x^2+y^2=100} that passes through (1,7) and subtends an angle \mathrm{\frac{2 \pi}{3}} at the origin. Then the angle between these two chords is
 

Option: 1

\mathrm{ \frac{\pi}{6}}


Option: 2

\mathrm{ \frac{\pi}{4}}


Option: 3

\mathrm{ \frac{\pi}{3}}


Option: 4

\mathrm{ \frac{\pi}{2}}


Answers (1)

best_answer


Let \mathrm{D}  be the midpoint of chord \mathrm{AB}, then

\mathrm{OD}=\mathrm{r} \cos \frac{\pi}{3}=5

Let equation of the chord A B be \mathrm{y-7=m(x-1) \Rightarrow y-m x+m-7=0}

\Rightarrow \mathrm{OD}=\frac{|\mathrm{m}-7|}{\sqrt{1+\mathrm{m}^2}}=5 \Rightarrow \mathrm{m}=\frac{3}{4}, \frac{-4}{3} \Rightarrow \mathrm{m}_1 \cdot \mathrm{m}_2=-1

Posted by

Gaurav

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