Home
Class 12
MATHS
In an acute angle triangle ABC, AD, BE a...

In an acute angle triangle ABC, AD, BE and CF are the altitudes, then `(EF)/a+(FD)/b+(DE)/c` is equal to -

Text Solution

Verified by Experts

`(FE)/(a) + (FD)/(b) + (DE)/(c) = (a cos A)/(a) + (b cos B)/(b) + (c cos C)/(a)`
`= cos A + cos B + cos C`
`le (3)/(2)`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.10|8 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.11|4 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.8|7 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise ARCHIVES (MATRIX MATCH TYPE )|1 Videos

  • PROPERTIES OF TRIANGLE, HEIGHT AND DISTANCE

    CENGAGE|Exercise Question Bank|32 Videos

Similar Questions

Explore conceptually related problems

In triangle ABC, AD, BE and CF are altitudes. Prove I, that, AD + BE + CF lt AB + BC + CA

In an acute angled triangle ABC, let AD,BE and CF be the perpendicular opposite sides of the triangle.The ratio of the product of the side lengths of the triangles DEF and ABC, is equal to

In an acute angled triangle ABC, A A_(1) and A A_(2) are the medians and altitudes respectively. Length A_(1) A_(2) is equal to

In two triangle ABC and DEF, AB= DE ,BC=DF and AC =Ef then

If in a Delta ABC, AD, BE and CF are the altitudes and R is the circumradius, then find the radius of the DEF.