Let the lengths of the altitudes from the vertices A - 1,1 , B 5,2 , C 3 , - 1 of Δ A B C are p 1 , p 2 , p 3 units respectively, then the value of 1 p 1 2 + 1 p 3 2 1 p 2 2 is equal to

Question

Let the lengths of the altitudes from the vertices A - 1,1 , B 5,2 , C 3 , - 1 of Δ A B C are p 1 , p 2 , p 3 units respectively, then the value of 1 p 1 2 + 1 p 3 2 1 p 2 2 is equal to,

MARKS App · Accepted Answer

1 p 1 2 + 1 p 3 2 1 p 2 2 = 2 Δ p 1 2 + 2 Δ p 3 2 2 Δ p 2 2 = B C 2 + A B 2 A C 2 {where Δ represents the area of triangle A B C } = 4 + 9 + 36 + 1 16 + 4 = 50 20 = 2 . 5

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