Home
Class 12
MATHS
For a triangle ABC, R = (5)/(2) and r = ...

For a triangle `ABC, R = (5)/(2) and r = 1`. Let D, E and F be the feet of the perpendiculars from incentre I to BC, CA and AB, respectively. Then the value of `((IA) (IB)(IC))/((ID)(IE)(IF))` is equal to _____

A

`(5)/(2)`

B

`(5)/(4)`

C

`(1)/(10)`

D

`(1)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
C

`rArr AI^(2) = (IE.IF)/(sin^(2)(A//2))`
`rArr (ID.IE.IF)/(IA.IB.IC) = sin.(A)/(2) sin.(B)/(2)sin.(C)/(2) = (r)/(4R) = (1)/(10)`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise (Multiple)|24 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise (Comprehension)|34 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.11|4 Videos

  • PROGRESSION AND SERIES

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

  • PROPERTIES OF TRIANGLE, HEIGHT AND DISTANCE

    CENGAGE|Exercise Question Bank|15 Videos

Similar Questions

Explore conceptually related problems

For triangle ABC,R=5/2 and r=1. Let I be the incenter of the triangle and D,E and F be the feet of the perpendiculars from I->BC,CA and AB, respectively. The value of (IDXIEXIF)/(IAXIBXIC) is equal to (a) 5/2 (b) 5/4 (c) 10 (d) 1/5

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)

In a acute angled triangle ABC, proint D, E and F are the feet of the perpendiculars from A,B and C onto BC, AC and AB, respectively. H is orthocentre. If sinA=3/5a n dB C=39 , then find the length of A H

Let A B C be a triangle with incenter I and inradius rdot Let D ,E ,a n dF be the feet of the perpendiculars from I to the sides B C ,C A ,a n dA B , respectively. If r_1,r_2a n dr_3 are the radii of circles inscribed in the quadrilaterals A F I E ,B D I F ,a n dC E I D , respectively, prove that (r_1)/(r-1_1)+(r_2)/(r-r_2)+(r_3)/(r-r_3)=(r_1r_2r_3)/((r-r_1)(r-r_2)(r-r_3))

Let A, B, and C be the vertices of a triangle. Let D, E, and F be the midpoints of the sides BC, CA, and AB respectively. Show that vec(AD)+vec(BE)+vec(CF)=vec(0) .

Circumradius of DeltaABC is 3 cm and its area is 6 cm^(2) . If DEF is the triangle formed by feet of the perpendicular drawn from A,B and C on the sides BC, CA and AB, respectively, then the perimeter of DeltaDEF (in cm) is _____

Let A B C be a triangle with incentre at Idot Also, let Pa n dQ be the feet of perpendiculars from AtoB Ia n dC I , respectively. Then which of the following results are correct? (A P)/(B I)=(sinB/2cosC/2)/(sinA/2) (b) (A Q)/(C I)=(sinC/2cosB/2)/(sinA/2) (A P)/(B I)=(sinC/2cosB/2)/(sinA/2) (d) (A P)/(B I)+(a Q)/(C I)=sqrt(3)if/_A=60^0

ABC is a right triangle right angled at C. Let BC = a, CA = b, AB = c and let p be the length of perpendicular from C on AB. Prove that (i) pc = ab (ii) (1)/(p^(2)) = (1)/(a^(2)) + (1)/(b^(2)) .

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

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.CH = 3 and (AH)^(2) + (BH)^(2) + (CH)^(2) = 7 Then answer the following Value of HD.HF is

CENGAGE-PROPERTIES AND SOLUTIONS OF TRIANGLE-Exercise (Single)
  1. The rational number which equals the number bar(2. 357) with recurri...

    Text Solution

    |

  2. Let A D be a median of the A B Cdot If A Ea n dA F are medians of the...

    Text Solution

    |

  3. For a triangle ABC, R = (5)/(2) and r = 1. Let D, E and F be the feet ...

    Text Solution

    |

  4. In triangle A B C ,/A=60^0,/B=40^0,a n d/C=80^0dot If P is the center ...

    Text Solution

    |

  5. If H is the othrocenter of an acute angled triangle ABC whose circumci...

    Text Solution

    |

  6. In triangle ABC, the line joining the circumcenter and incenter is ...

    Text Solution

    |

  7. In triangle ABC, line joining the circumcenter and orthocentre is p...

    Text Solution

    |

  8. In triangle A B C ,/C=(2pi)/3 and C D is the internal angle bisector o...

    Text Solution

    |

  9. In the given figure DeltaABC is equilateral on side AB produced. We ch...

    Text Solution

    |

  10. A variable triangle A B C is circumscribed about a fixed circle of uni...

    Text Solution

    |

  11. In A B C ,ifa=10a n dbcotB+c cot C=2(r+R) then the maximum area of A...

    Text Solution

    |

  12. Let C be incircle of A B Cdot If the tangents of lengths t1,t2a n dt3...

    Text Solution

    |

  13. A park is in the form of a rectangle 120 mx100 mdot At the centre of t...

    Text Solution

    |

  14. In triangle ABC, if r(1) = 2r(2) = 3r(3), then a : b is equal to

    Text Solution

    |

  15. If in a triangle (1-(r1)/(r2))(1-(r1)/(r3))=2 then the triangle is rig...

    Text Solution

    |

  16. If in a triangle (r)/(r(1)) = (r(2))/(r(3)), then

    Text Solution

    |

  17. In Delta ABC, I is the incentre, Area of DeltaIBC, DeltaIAC and DeltaI...

    Text Solution

    |

  18. In an acute angled triangle A B C ,r+r1=r2+r3a n d/B >pi/3, then b+2c...

    Text Solution

    |

  19. If in triangle A B C ,sumsinA/2=6/5a n dsumI I1=9 (where I1,I2a n dI3 ...

    Text Solution

    |

  20. The radii r1, r2,r3 of the escribed circles of the triangle A B C are ...

    Text Solution

    |