Home
Class 11
MATHS
If the distance between incenter and one...

If the distance between incenter and one of the excenter of an equilateral triangle is 4 units, then find the inradius of the triangle.

Text Solution

Verified by Experts

`I*I_1=4R*sin(A/2)=4`
`4=4R*1/2`
`R=2`
`R=2r`
`r=1 unit`.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

The circum radius of an equilateral triangle is 4cm. Find the inner radius of the triangle.

If the height of an equilateral triangle be be 15 cm, then find the perimeter and area of triangle.

write the ratio of the angles of an equilateral triangle.

The area of an equilateral triangle is 4sqrt(3)cm^(2). Then the of each of the sides of the triangle is

The length of the sides of an equilateral Delta ABC is 2 a units.Find the height of the triangle.

The equation to the base of an equilateral triangle is x+y=2and its vertex is at (2,-1) . Find the length of a side of the triangle.

Construct an equilateral triangle with side 6 cm. Draw the in circle of this triangle.

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS-All Questions
  1. Let f(theta)=1/(1+(cottheta)^2) , and S=sum(theta=1^0)^(89^0)f(theta),...

    Text Solution

    |

  2. The number of values of theta in the interval (-pi/2,pi/2) satisfying ...

    Text Solution

    |

  3. If the distance between incenter and one of the excenter of an equi...

    Text Solution

    |

  4. The value of 3(sin^4t+cos^4t-1)/(sin^6t+cos^6t-1) is equal to

    Text Solution

    |

  5. Number of roots of the equation 2^(tan(x-pi/4))-2(0. 25)^((sin^2(x-pi...

    Text Solution

    |

  6. If sintheta-costheta=1, then the value of sin^3theta-cos^3theta is

    Text Solution

    |

  7. Given a triangle A B C with sides a=7, b=8 and c=5. Find the value of ...

    Text Solution

    |

  8. The smallest positive value of x (in radians) satisfying the equation...

    Text Solution

    |

  9. In convex quadrilateral A B C D ,A B=a ,B C=b ,C D=c ,D A=d . This qua...

    Text Solution

    |

  10. Suppose that for some angles xa n dy , the equations sin^2x+cos^2y=(3a...

    Text Solution

    |

  11. The number of distinct real roots of the equation tan(2pix)/(x^2+x+1)=...

    Text Solution

    |

  12. In a cyclic quadrilateral PQRS, PQ= 2 units, QR= 5 units, RS=3 units ...

    Text Solution

    |

  13. The number of solution of the equation sin2theta-2costheta+4sintheta=4...

    Text Solution

    |

  14. If 0 lt x lt 5/4 and cosx+sinx=5/4 then the value of 16(cosx-sinx)^2 i...

    Text Solution

    |

  15. If Delta represents the area of acute angled triangle ABC, then sqrt(a...

    Text Solution

    |

  16. In Triangle A B C ,B C=8,C A=6a n dA B=10. A line dividing the triangl...

    Text Solution

    |

  17. If 1/6sintheta,costheta,tantheta are in GdotPdot, then theta is equ...

    Text Solution

    |

  18. If the angles of a triangle are 30^0a n d45^0 and the included side is...

    Text Solution

    |

  19. The number of solutions of equation 6cos2theta+2cos^2(theta/2)+2sin^2t...

    Text Solution

    |

  20. The circumference of a circle circumscribing an equilateral triangle i...

    Text Solution

    |