Home
Class 12
MATHS
A circle is inscribed in a triangle A B ...

A circle is inscribed in a triangle `A B C` touching the side `A B` at `D` such that `A D=5,B D=3,if/_A=60^0` then length `B C` equals. (a) 4 (b)`(120)/(13)`(c) `13`(d) `12`

A

9

B

`(120)/(13)`

C

13

D

12

Text Solution

Verified by Experts

The correct Answer is:
C

`tan 30^(@) = (r)/(5)`
or `r = (5)/(sqrt3)`
We have `tan.(B)/(2) = (r)/(3) = (5)/(3sqrt3)`...(i)
`:. cos B (1-tan^(2).(B)/(2))/(1+tan^(2).(B)/(2)) = (1)/(26)`
`:. sin B = (sqrt(675))/(26) = (15 sqrt3)/(26)`
`:. sin C = sin (A +B) = sin A cos B + cos A sin B = (4sqrt3)/(13)`
Now `(a)/(sinA) = (c)/(sinC) rArr a = 13`
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

Let a and b represent the lengths of a right triangles legs. If d is the diameter of a circle inscribed into the triangle, and D is the diameter of a circle circumscribed on the triangle, the d+D equals. (a) a+b (b) 2(a+b) (c) 1/2(a+b) (d) sqrt(a^2+b^2)

A circle of radius 4cm is inscribed in A B C , which touches the side B C a t Ddot If B D=6c m ,D C=8c m then (a) the triangle is necessarily acute angled (b) tan(A/2)=4/7 (c) perimeter of the triangle A B C is 42c m (d) area of A B C is 84c m^2

If an a triangle A B C , b=3 c, a n d C-B=90^0, then find the value of tanB

In a scalene triangle A B C ,D is a point on the side A B such that C D^2=A D * D B , sin sin A * Sin B=sin^2C/2 then prove that CD is internal bisector of /_Cdot

Let D be the middle point of the side B C of a triangle A B Cdot If the triangle A D C is equilateral, then a^2: b^2: c^2 is equal to 1:4:3 (b) 4:1:3 (c) 4:3:1 (d) 3:4:1

In triangle A B C ,/_A=30^0,H is the orthocenter and D is the midpoint of B C . Segment H D is produced to T such that H D=D T The length A T is equal to (a). 2B C (b). 3B C (c). 4/2B C (d). none of these

Let A B C D be a quadrilateral with area 18 , side A B parallel to the side C D ,a n dA B=2C D . Let A D be perpendicular to A Ba n dC D . If a circle is drawn inside the quadrilateral A B C D touching all the sides, then its radius is a = 3 (b) 2 (c) 3/2 (d) 1

In triangle A B C ,/_A=60^0,/_B=40^0,a n d/_C=80^0dot If P is the center of the circumcircle of triangle A B C with radius unity, then the radius of the circumcircle of triangle B P C is (a) 1 (b) sqrt(3) (c) 2 (d) sqrt(3) 2

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 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) 2RsinAsinBsinC (d) Δ /R

CENGAGE PUBLICATION-PROPERTIES AND SOLUTIONS OF TRIANGLE-Exercises
  1. In triangle A B C ,ifA-B=120^0a n dR=8r ,w h e r eRa n dr have their u...

    Text Solution

    |

  2. A B C is an equilateral triangle of side 4c mdot If R , r, a n d,h are...

    Text Solution

    |

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

    Text Solution

    |

  4. The rational number which equals the number 2. 126 with recurring de...

    Text Solution

    |

  5. AD is a median of the DeltaABC.If AE and AFare medians of the triangle...

    Text Solution

    |

  6. For triangle ABC,R=5/2 and r=1. Let I be the incenter of the triangle ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. In triangle ABC,angleC=(2pi)/3 and CD is the internal angle bisector ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |