If the orthocentre and circumcentre of a tria | vedclass

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(A) Let $O$ be the orthocentre and $C'$ be the circumcentre of $	riangle ABC$.The distance of the orthocentre $O$ from side $BC$ is given by $ON = 2R

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$3$

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(A) Let $O$ be the orthocentre and $C'$ be the circumcentre of $	riangle ABC$.The distance of the orthocentre $O$ from side $BC$ is given by $ON = 2R \cos B \cos C$.The distance of the circumcentre $C'$ from side $BC$ is given by $C'M = R \cos A$.Given that $ON = C'M$,we have:$2R \cos B \cos C = R \cos A$$2 \cos B \cos C = \cos A$Since $A + B + C = 180^{\circ}$,$\cos A = \cos(180^{\circ} - (B + C)) = -\cos(B + C)$.Thus,$2 \cos B \cos C = -\cos(B + C)$.$2 \cos B \cos C = -(\cos B \cos C - \sin B \sin C)$.$2 \cos B \cos C = -\cos B \cos C + \sin B \sin C$.$3 \cos B \cos C = \sin B \sin C$.Dividing both sides by $\cos B \cos C$ (assuming $\cos B, \cos C 
eq 0$):$3 = 	an B 	an C$.Therefore,$	an B 	an C = 3$.

If the orthocentre and circumcentre of a triangle $ABC$ are at equal distances from the side $BC$ and lie on the same side of $BC$,then the value of $\tan B \tan C$ is equal to:

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