Home
Class 11
MATHS
Let A B C be a triangle with incenter I ...

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))`

Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

Let ABC be a triangle with incentre I and inradius r. Let D, E, F be the feet of the perpendiculars from I to the sides BC, CA and AB, respectively, If r_(2)" and "r_(3) are the radii of circles inscribed in the quadrilaterls AFIE, BDIF and CEID respectively, then prove that r_(1)/(r-r_(1))+r_(2)/(r-r_(2))+r_(3)/(r-r_(3))=(r_(1)r_(2)r_(3))/((r-r_(1))(r-r_(2))(r-r_(3)))

If r/(r_1)=(r_2)/(r_3), then

Prove that (r_(1) -r)/(a) + (r_(2) -r)/(b) = (c)/(r_(3))

Prove that nC_r+3.nC_(r-1)+3nC_(r-2)+nC_(r-3)=(n+3)C_r

Prove that r_1+r_2+r_3-r=4R

Let the incircle with center I of A B C touch sides BC, CA and AB at D, E, F, respectively. Let a circle is drawn touching ID, IF and incircle of A B C having radius r_2dot similarly r_1a n dr_3 are defined. Prove that (r_1)/(r-r_1)dot(r_2)/(r-r_2)dot(r_3)/(r-r_3)=(a+b+c)/(8R)

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 (ID*IE*IF)/(IA*IB*IC) is equal to (a) 5/2 (b) 5/4 (c) 1/10 (d) 1/5

Prove that r_(1) r_(2) + r_(2) r_(3) + r_(3) r_(1) = (1)/(4) (a + b + c)^(2)

Prove that , .^(n)C_(r)+3.^(n)C_(r-1)+3.^(n)C_(r-2)+^(n)C_(r-3)=^(n+3)C_(r)

Prove that (r+r1)tan((B-C)/2)+(r+r2)tan((C-A)/2)+(r+r3)tan((A-B)/2)=0

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS-All Questions
  1. Solve 2cos^2theta+sinthetalt=2, where pi/2lt=thetalt=(3pi)/2dot

    Text Solution

    |

  2. Evaluate the sine of each of the following angles without using a ca...

    Text Solution

    |

  3. Let A B C be a triangle with incenter I and inradius rdot Let D ,E ,a ...

    Text Solution

    |

  4. Prove that the least positive value of x , satisfying tanx=x+1,lies i...

    Text Solution

    |

  5. Find the reference angles corresponding to each of the following ang...

    Text Solution

    |

  6. If Delta is the area of a triangle with side lengths a, b, c, then s...

    Text Solution

    |

  7. Suppose the point with coordinates (-12, 5) is on the terminal side of...

    Text Solution

    |

  8. If ma n dn(n > m) are positive integers, then find the number of solut...

    Text Solution

    |

  9. I(n) is the area of n sided refular polygon inscribed in a circle unit...

    Text Solution

    |

  10. Solve 3tan2x-4tan3x=tan^2 3xtan2xdot

    Text Solution

    |

  11. Assuming the distance of the earth from the moon to be 38,400 km and ...

    Text Solution

    |

  12. Let the angles A , Ba n dC of triangle A B C be in AdotPdot and let b ...

    Text Solution

    |

  13. Find the angle between the minute hand and the hour hand of a clock ...

    Text Solution

    |

  14. For which values of a does the equation 4sin(x+pi/3)cos(x-pi/6)=a^2+sq...

    Text Solution

    |

  15. In a triangle of base a, the ratio of the other sides is r(lt1). Show...

    Text Solution

    |

  16. Solve sintheta+sqrt(3)costheta ge1,-pilttheta ltpi

    Text Solution

    |

  17. For each natural number k, let Ck denotes the circle with radius k uni...

    Text Solution

    |

  18. Let A,B,C, be three angles such that A=pi/4 and tanB tanC=pdot Find ...

    Text Solution

    |

  19. Solve cos2x >|sinx|,x in (pi/2,pi)

    Text Solution

    |

  20. State if the given angles are coterminal. (i) alpha=185^0,beta=-545^0 ...

    Text Solution

    |