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. 9 (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 ENGLISH|Exercise Multiple correct answer type|24 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Linked comprehension type|34 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Concept application exercise 5.11|4 Videos

  • PROGRESSION AND SERIES

    CENGAGE ENGLISH|Exercise ARCHIVES (MATRIX MATCH TYPE )|1 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise Archives(Matrix Match Type)|1 Videos

Similar Questions

Explore conceptually related problems

9+|-4| is equal to: (a)5 (b) -5 (c) 13 (d) -13

In a triangle A B C , if A B=A C\ a n d\ A B is produced to D such that B D=B C , find /_A C D\ :\ /_A D C

In an equilateral triangle A B C the side B C is trisected at D . Prove that 9\ A D^2=7\ A B^2

Side B C of a triangle A B C has been produced to a point D such that ∠ACD = 120^0dot If /_B=1/2/_A , then /_A is equal to 80^0 (b) 75^0 (c) 60^0 (d) 90^0

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)

D is a point on the side BC of a triangle ABC such that /_A D C=/_B A C . Show that C A^2=C B.C D .

A point D is on the side B C of an equilateral triangle A B C such that D C=1/4\ B C . Prove that A D^2=13\ C D^2 .

A circle touches all the four sides of a quadrilateral A B C D . Prove that: A B+C D=B C+D A .

Two circles are drawn with sides A B ,A C of a triangle A B C as diameters. The circles intersect at a point D . Prove that D lies on B C .

In Figure, A B C D is quadrilateral inscribed in a circle with centre O. C D is produced to E such that /_A DE=95^0a n d\ /_O B A=30^0. Find /_O A C .

CENGAGE ENGLISH-PROPERTIES AND SOLUTIONS OF TRIANGLE-Exercises
  1. In triangle ABC, if A - B = 120^(2) and R = 8r, where R and r have the...

    Text Solution

    |

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

    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. 357 with recurring de...

    Text Solution

    |

  5. Let AD be a median of the Delta ABC. If AE and AF are medians of the t...

    Text Solution

    |

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

    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 par...

    Text Solution

    |

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

    Text Solution

    |

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

    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 Delta ABC, if a = 10 and b cot B + c cot C = 2(r + R) then the maxi...

    Text Solution

    |

  15. Let C be incircle of DeltaABC. If the tangents of lengths t(1),t(2) an...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. If in a triangle, (1-(r(1))/(r(2))) (1 - (r(1))/(r(3))) = 2, then the ...

    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

    |