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In triangle $A B C$ the equation of side $B C$ is $2 x - y = 3$ and its circumcentre and orthocentre are at (2,d) and (1,2) respectively then match the items of column I with items of column II

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Tan B Tan C p

The length of BC q

Sin A

Area of the triangle is

$\frac{4 \sqrt{13}}{\sqrt{5}}$

$\frac{18 \sqrt{13}}{5}$

$3$

$\frac{2 \sqrt{13}}{\sqrt{61}}$

answer is A, .

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Detailed Solution

The line joining the orthocentre and circum-centre is parallel to the side $B C$ . Distance from orthocentre to the vertex $A$ is $2 R C o s A$ and the distance from
orthocentre to side $B C$ is $2 R C o s B C o s C$

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