Question
Question: If \(p _ { 1 } , p _ { 2 } , p _ { 3 }\) are altitudes of a triangle ABC from the vertices A, B, C a...
If p1,p2,p3 are altitudes of a triangle ABC from the vertices A, B, C and Δ, the area of the triangle, then p1−2+p2−2+p3−2 is equal to
A
Δa+b+c
B
4Δ2a2+b2+c2
C
Δ2a2+b2+c2
D
None
Answer
4Δ2a2+b2+c2
Explanation
Solution
We have 21ap1=Δ,21bp2=Δ,21cp3=Δ
⇒ p1=a2Δ,p2=b2Δ,p3=c2Δ
∴ p121+p221+p321=4Δ2a2+b2+c2.