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  • The triangle PQR is inscribed in the circle  If Q and R hav

The triangle PQR is inscribed in the circle \mathrm{x^2+y^2=25} If Q and R have coordinates (3, 4), (–4, 3) respectively, then < Q PR =

Option: 1

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


Option: 2

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


Option: 3

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


Option: 4

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


Answers (1)

best_answer

The centre O is (0, 0) 

\mathrm{(Slope of O R) .( Slope of O Q)=\left(\frac{3}{-4}\right)\left(\frac{4}{3}\right)=-1}

\mathrm{\Rightarrow \quad<R O Q=90^{\circ}}

However, the angle at the centre is double the angle at the circumference.
For point P on the circumference of the circle,

\mathrm{<R P Q=\frac{1}{2}(<R O Q)=\frac{90}{2}=45^{\circ}}

Posted by

SANGALDEEP SINGH

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