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If P(1),P(2),P(3) are the altitudes of t...

If `P_(1),P_(2),P_(3)` are the altitudes of the `DeltaABC` then , show that `(1)/(P_(1)^(2))+(1)/(P_(2)^(2))+(1)/(P_(3)^(2))=(cotA+cotB+cotC)/(Delta)`

A

`(2ab cos^(2)C//2)/(Delta(a+b+c))`

B

`(1)/(R)`

C

`(cotA+cotB+cotC)/(Delta)`

D

2R

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-PROPERTIES OF TRIANGLES-PRACTICE SHEET (EXERCISE-III) (LEVEL-I) (Straight Objective Type Questions)
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  7. If a = 18 , b=24 , c=30 , find r(1) .

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  8. In DeltaABC, if C=90^(@) then R+r=

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  9. In DeltaABC,sqrt(rr1r2r3)/(2Rr(sinA+sinB+sinC)) =

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  14. The radius of the circle passing through the centre of incircle of Del...

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  16. In a Delta ABC if angle A=90^@, then cos^(-1)(( R)/(r2 +r3)) is equal

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  17. If alpha,beta,gamma, are lengths of the altitudes of a triangle ABC wi...

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  18. If P(1),P(2),P(3) are the altitudes of the DeltaABC then , show that ...

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  19. The sides of a cyclic quadrilateral are 3,3,4,4 when its area is great...

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