Home
Class 12
MATHS
Consider an acute angled Delta ABC. Let ...

Consider an acute angled `Delta ABC.` Let AD, BE and CF be the altitudes drawn from the vertice to the opposite sides. Prove that : `(EF)/(a)+ (FD)/(b)+ (DE)/(c)= (R+r)/(R ).`

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 PUBLICATION|Exercise Concept application exercise 5.10|8 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Concept application exercise 5.11|4 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Concept application exercise 5.8|7 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE )|8 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1119 Videos

Similar Questions

Explore conceptually related problems

Prove analytically that in any triangle the perpendiculars drawn from the vertices upon the opposite sides are concurrent.

If in a DeltaABC, the altituds drawn from the vertices A,B, C on opposite sides are in H.P., then sin A, sin B, sin C are in-

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

Let f, g and h be the lengths of the perpendiculars from the circumcenter of Delta ABC on the sides a, b, and c, respectively. Prove that (a)/(f) + (b)/(g) + (c)/(h) = (1)/(4) (abc)/(fgh)

If in a triangle ABC, AD, BE and CF are the attitude and R is the circum-radius then find the radius of circle circumscribing the triangle DEF.

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)) .

The diameters of the circumcirle of triangle ABC drawn from A,B and C meet BC, CA and AB, respectively, in L,M and N. Prove that (1)/(AL) + (1)/(BM) + (1)/(CN) = (2)/(R)

Let the lengths of the altitudes drawn from the vertices of Delta ABC to the opposite sides are 2, 2 and 3. If the area of Delta ABC " is " Delta , then find the area of triangle

Let ABC be an acute angled triangle with orthocenter H.D, E, and F are the feet of perpendicular from A,B, and C, respectively, on opposite sides. Also, let R be the circumradius of DeltaABC . Given AH.BH.CH = 3 and (AH)^(2) + (BH)^(2) + (CH)^(2) = 7 Then answer the following Value of R is

If x,y,z are the perpendiculars from the vertices of a triangle ABC on the opposite sides a,b,c respectively, then show that (bx)/c+(cy)/a+(az)/b=(a^2+b^2+c^2)/(2R)