Any circle passing through the point of inter | vedclass

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(A) Let the two lines be $L_1: x + \sqrt{3}y - 1 = 0$ and $L_2: \sqrt{3}x - y - 2 = 0$.The slopes of these lines are $m_1 = -\frac{1}{\sqrt{3}}$ and $

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$180$

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(A) Let the two lines be $L_1: x + \sqrt{3}y - 1 = 0$ and $L_2: \sqrt{3}x - y - 2 = 0$.The slopes of these lines are $m_1 = -\frac{1}{\sqrt{3}}$ and $m_2 = \sqrt{3}$.Since $m_1 	imes m_2 = -\frac{1}{\sqrt{3}} 	imes \sqrt{3} = -1$,the lines are perpendicular to each other.Let the point of intersection be $R$. Since the lines are perpendicular,the angle between them at $R$ is $	heta = 90^{\circ}$.In a circle,the angle subtended by an arc at the centre is twice the angle subtended by the same arc at any point on the remaining part of the circle.Therefore,the angle subtended by the arc $PQ$ at the centre is $2 	imes 90^{\circ} = 180^{\circ}$.

Any circle passing through the point of intersection of the lines $x + \sqrt{3}y = 1$ and $\sqrt{3}x - y = 2$ intersects these lines at points $P$ and $Q$. The angle subtended by the arc $PQ$ at its centre is- ............. $^o$

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