Properties of Triangles 2 Question 16

16. If p1,p2,p3 are the perpendiculars from the vertices of a triangle to the opposite sides, then prove that

p1p2p3=a2b2c28R3

(1978, 3M)

Integer Answer Type Question

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Solution:

  1. We know that, Δ=12ap1

p1=2Δa

Similarly, p2=2Δb and p3=2Δc

Now,

p1p2p3=8Δ3abc

Since, Δ=abc4R

p1p2p3=8abc(abc)364R3=(abc)28R3



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