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The three sides of a triangle are L(r) +...

The three sides of a triangle are `L_(r) + x cos theta_(r) + y sin theta _(r) - p_(r) = 0 ` where r = 1,2,3 . Show that the orthocentre is given by
`L_(1) cos (theta_(2)-theta_(3)) = L_(2)cos (theta_(3)-theta_(1)) = L_(3)cos (theta_(1)-theta_(2))` .

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