Home
Class 12
MATHS
If in a triangle (1-r1/r2)(1-r1/r3)=2,th...

If in a triangle `(1-r_1/r_2)(1-r_1/r_3)=2,`then the triangle is

A

right angled

B

isosceles

C

equilateral

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have `(1-(s-b)/(s-a)) (1-(s-c)/(s-a)) = 2`
or `2(b-a) (c-a) = 4 (s-a)^(2)`
or or `2(bc-ac -ab +a^(2)) = (2s-2a)^(2)`
or `a(bc-ac-ab+a^(2)) = (b+c -a)^(2)`
or `a^(2) = b^(2) + c^(2)`
Hence, triangle is right angled
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Multiple correct answer type|24 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Linked comprehension type|34 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Concept application exercise 5.11|4 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

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

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

If r_1 =r_2+r_3+r, prove that the triangle is right angled.

In triangle ABC, if r_(1) = 2r_(2) = 3r_(3) , then b : c is equal to

In triangle A B C , if r_1=2r_2=3r_3, then a : b is equal to 5/4 (b) 4/5 (c) 7/4 (d) 4/7

In DeltaABC, R, r, r_(1), r_(2), r_(3) denote the circumradius, inradius, the exradii opposite to the vertices A,B, C respectively. Given that r_(1) :r_(2): r_(3) = 1: 2 : 3 The sides of the triangle are in the ratio

If in a DeltaABC, r_1r_2+r_2r_3+r_3r_1 is equal to (where r_1,r_2,r_3 are the exradii and 2s is the perimeter)

Given that Delta = 6,r_1=2, r_(2) = 3, r_(3) = 6 then Inradius is equal to

In Delta ABC , if r_(1) lt r_(2) lt r_(3) , then find the order of lengths of the sides

In a triangle of base a, the ratio of the other two sides is r (lt 1) . Show that the altitude of the triangle is less than or equal to (ar)/(1-r^(2))

CENGAGE PUBLICATION-PROPERTIES AND SOLUTIONS OF TRIANGLE-Exercises
  1. A variable triangle A B C is circumscribed about a fixed circle of uni...

    Text Solution

    |

  2. In A B C ,if a=10 and bcotB+ c cotC=2(r+R) then the maximum area of ...

    Text Solution

    |

  3. Let C be incircle of A B Cdot If the tangents of lengths t1,t2 and t3...

    Text Solution

    |

  4. A park is in the form of a rectangle 120m x 100m At the centre of th...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. In an acute angled triangle A B C ,r+r1=r2+r3a n d/B >pi/3, then (a) b...

    Text Solution

    |

  10. If in triangle A B C ,sumsin(A/2)=6/5a n dsumI I1=9 (where I1,I2 a n d...

    Text Solution

    |

  11. The radii r(1), r(2), r(3) of the escribed circles of the triangle ABC...

    Text Solution

    |

  12. In ABC with usual notations, if r=1,r1=7 and R=3, the (a) ABC is equil...

    Text Solution

    |

  13. Which of the following expresses the circumference of a circle inscr...

    Text Solution

    |

  14. In A B C , the median A D divides /B A C such that /B A D :/C A D=2:1...

    Text Solution

    |

  15. The area of the circle and the area of a regular polygon inscribed th...

    Text Solution

    |

  16. The ratio of the area of a regular polygon of n sides inscribed in a c...

    Text Solution

    |

  17. In any triangle, the minimum value of r^(3) /(r(1) r(2) r(3)) is equal...

    Text Solution

    |

  18. If R1 is the circumradius of the pedal triangle of a given triangle A ...

    Text Solution

    |

  19. A sector O A B O of central angle theta is constructed in a circle wit...

    Text Solution

    |

  20. Triangle ABC is isosceles with AB=AC and BC=65cm. P is a point on BC s...

    Text Solution

    |