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If p(2),p(2),p(3) are the perpendiculars...

If `p_(2),p_(2),p_(3)` are the perpendiculars from the vertices of a triangle to the opposite sides, then prove that
`p_(1)p_(2)p_(3)=(a^(2)b^(2)c^(2))/(8R^(3))`

Text Solution

Verified by Experts

We know that `, Delta=(1)/(2)ap_(1)`
`rArr p_(1)=(2Delta)/(a)`
Similarly, `p_(2)=(2Delta)/(b) and p_(3)=(2Delta)/(c)`
Now, `p_(1)p_(2)p_(3)=(8Delta^(3))/(abc)`
Since `Delta=(abc)/(4R)`
`:. P_(1)p_(2)p_(3)=(8)/(abc)*((abc)^(8))/(6R^(3))=((abc)^(2))/(8R^(3))`
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