A) \[{{180}^{o}}\]
B) \[{{90}^{o}}\]
C) \[{{120}^{o}}\]
D) Depends on centre and radius
Correct Answer: A
Solution :
Let the point of intersection of two lines is A. \[\therefore \] The angle subtended by PQ on centre C \[=\]Two times the angle subtended by PQ on point A. For \[x+\sqrt{3}y=1\], \[{{m}_{1}}=\frac{-1}{\sqrt{3}}\] and For \[\sqrt{3}x-y=2,\] \[{{m}_{2}}=\sqrt{3}\] \[\because \]\[{{m}_{1}}\times {{m}_{2}}=\frac{-1}{\sqrt{3}}\times \sqrt{3}=-1\], \[\therefore \ \angle A={{90}^{o}}\] \[\therefore \]The angle subtended by arc PQ at its centre \[=2\times {{90}^{o}}={{180}^{o}}\] Trick: Given lines are perpendicular to each other, so PQ passes through centre of circle, hence arc makes \[{{180}^{o}}\] to centre.You need to login to perform this action.
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