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If the lengths of the perpendiculars from the vertices of a triangle ABC on the opposite sides are `p_(1), p_(2), p_(3)` then prove that `(1)/(p_(1)) + (1)/(p_(2)) + (1)/(p_(3)) = (1)/(r) = (1)/(r_(1)) + (1)/(r_(2)) + (1)/(r_(3))`.

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VMC MODULES ENGLISH-PROPERTIES OF TRIANGLE-Level - 2
  1. In any Delta ABC, show that cos A+ cos B+ cos C = (1+ (r )/(R )).

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  2. Prove that (r(2) + r(3))/(1 + cos A) = (r(3) + r(1))/(1 + cos B) =...

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  3. If the lengths of the perpendiculars from the vertices of a triangle A...

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  4. Prove that the distance of the incentre of Delta ABC from A is 4R si...

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  5. The sides of a triangle are three consecutive natural numbers and its ...

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  6. If A, A(1), A(2), A(3) are the areas of the inscribed and escribed of ...

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  7. If in a triangle, (1-(r(1))/(r(2))) (1 - (r(1))/(r(3))) = 2, then the ...

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  8. In a triangle Delta ABC, prove the following : 2 abc cos.(A)/(2) co...

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  9. In a triangle Delta ABC, prove the following : (tan A//2)/((a-b)(a-...

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  10. If the angle opf a triangle are in the ratio 1:2:3, then show that the...

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  11. If a cosA=b cos B, then prove that either the triangle is isosceles or...

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  12. If in Delta ABC, c(a+b) cos ""1/2 B=b (a+c) cos ""1/2 C, the triangle ...

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  13. Let A, B be two points on the bank of a straight river, and C, D point...

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  14. In the ambiguous case, it two triangles are formed with a, b, A, then ...

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  15. If x=2/3 and x=-3 are the roots of the equation a x^2+7x+b=0, find the...

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  16. Statement I In a Delta ABC, if a lt b lt c and r is inradius and r(1) ...

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  17. Statement I If the sides of a triangle are 13, 14 15 then the radius o...

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  18. Statement I In a DeltaABC, sum (cos ^(2)""(A)/(2))/(a ) has the value...

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  19. If the sides of a triangle are in A.P., and its greatest angle exceeds...

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  20. If r(1), r(2) ,r(3) are the ex-radii of DeltaABC, then prove that (b...

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