Home
Class 12
MATHS
A B C is an equilateral triangle of side...

`A B C` is an equilateral triangle of side `4c mdot` If `R ,ra n dh` are the circumradius, inradius, and altitude, respectively, then `(R+h)/h` is equal to 4 (b) 2 (c) 1 (d) 3

A

4

B

2

C

1

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
In equilateral triangle, circumcenter (O) and incenter (I) coincide

Also from the diagram,
`R + r = h " or " (R +r)/(h) = 1`
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

In triangle A B C , let /_c=pi/2dot If r is the inradius and R is circumradius of the triangle, then 2(r+R) is equal to (a) a+b (b) b+c (c) c+a (d) a+b+c

In triangle A B C , let /_c=pi/2dot If r is the inradius and R is circumradius of the triangle, then 2(r+R) is equal to a+b (b) b+c c+a (d) a+b+c

In triangle A B C , if cosA+cosB+cosC=7/4, t h e n R/r is equal to 3/4 (b) 4/3 (c) 2/3 (d) 3/2

In an equilateral triangle, the inradius, circumradius, and one of the exradii are in the ratio a)2:4:5 (b) 1:2:3 (c) 1:2:4 (d) 2:4:3

Let A B C be a triangle having O and I as its circumcenter and incentre, respectively. If R and r are the circumradius and the inradius, respectively, then prove that (O I)^2=R^2-2R rdot Further show that the triangle B I O is a right angled triangle if and only if b is arithmetic mean of a and c.

In triangle A B C , if r_1=2r_2=3r_2, then a : b is equal to 5/4 (b) 4/5 (c) 7/4 (d) 4/7

In a triangle with sides a,b,c,r_1 gt r_2 gt r_3 ( which are the ex - radii ) then

In acute angled triangle A B C ,A D is the altitude. Circle drawn with A D as its diameter cuts A Ba n dA Ca tPa n dQ , respectively. Length of P Q is equal to /(2R) (b) (a b c)/(4R^2) (c) 2RsinAsinBsinC (d) delta/R

Given an isoceles triangle with equal side of length b and angle alpha lt pi//4 , then the circumradius R is given by

Given an isoceles triangle with equal side of length b and angle alpha lt pi//4 , then the inradius r is given by

CENGAGE-PROPERTIES AND SOLUTIONS OF TRIANGLE-Exercise (Single)
  1. Given b=2,c=sqrt(3),/A=30^0 , then inradius of A B C is (sqrt(3)-1)/2...

    Text Solution

    |

  2. In triangle A B C ,ifA-B=120^0a n dR=8r ,w h e r eRa n dr have their u...

    Text Solution

    |

  3. A B C is an equilateral triangle of side 4c mdot If R ,ra n dh are the...

    Text Solution

    |

  4. A circle is inscribed in a triangle A B C touching the side A B at D s...

    Text Solution

    |

  5. The rational number which equals the number bar(2. 357) with recurri...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |