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If P(1),P(2),P(3) are altitudes of a Del...

If `P_(1),P_(2),P_(3)` are altitudes of a `DeltaABC` then show that
`(1)/(P_(1))+(1)/(P_(2))-(1)/(P_(3))=(1)/(r_(3))`

A

`1/r`

B

`1/r_(1)`

C

`1/r_(2)`

D

`1/r_(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
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AAKASH SERIES-PROPERTIES OF TRIANGLES-LECTURE SHEET EXERCISE - III (Straight Objective Type Question)
  1. A triangle has sides 6,7 and 8. The line through its incentre parallel...

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  2. If p(1), p(2), p(3) are respectively the perpendiculars from the verti...

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

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  4. If p(1), p(2), p(3) are respectively the perpendiculars from the verti...

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  5. If p(1), p(2), p(3) are respectively the perpendiculars from the verti...

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  6. The legs of a right triangle are a and b the linc segment of length d ...

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  7. The length of medians of a Delta^("le") ABC are 6, 8 , 10 then its ar...

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  8. In DeltaABC if r(1)=2r(1)=3r(3) and D is the mid point of BC then cos ...

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  9. In DeltaABC, if a=7 b=8, c=9 then the distance from the vertex B to th...

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  10. In triangle ABC, medians AD and CE are drawn. If AD = 5, angle DAC = p...

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  11. If the median of DeltaABC through A is perpendicular to AB then tan A+...

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  12. Let l(1), l(2), l(3) be the lengths of the internal bisectors of angle...

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  13. In trianle ABC, CD is the bisector of the angle C. if cos . C/2 = 1/3 ...

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  14. If AD, BE , CF are internal bisectors of the angles of Delta ABC, " th...

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  15. If two shorter sides of a triangle measure 9 and 18. If the internal a...

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  16. The internal angular bisectors of angles of a Delta^("le") ABC meets c...

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  17. In a triangle ABC bisector of lfloor C meets the side AB at D and circ...

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  18. In Delta ABC , the median AD divides angle BAC such that angle BAD : ...

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  19. In a triangle ABC, the median to the side BC is of length 1/sqrt(11 - ...

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  20. If AD, BE and CF are the medians of a triangle ABC, then AD^(2) + BE^(...

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