In a triangle ABC , the equation of side BC is 2 x − y = 3 and its circumcentre and orthocenter are at ( 2 , 4 ) and ( 1 , 2 ) respectively. The value of sin B sin C is equal to

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R cos A = 5 ​ 3 ​ ⇒ − R cos B cos C + R sin B sin C = 5 ​ 3 ​ and 2 R cos B cos C = 5 ​ 3 ​ . Adding: R sin B sin C = 5 ​ 3 ​ + 2 5 ​ 3 ​ = 2 5 ​ 9 ​ ⇒ sin B sin C = 2 5 ​ ⋅ 5 61 ​ ​ 9 ​ = 2 61 ​ 9 ​ .

Mathematics - Properties of Triangle Question with Solution | TestHub

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