Home
Class 12
MATHS
DeltaABC is equilateral triangle of side...

`DeltaABC` is equilateral triangle of side a. P lies on AB such that A is midpoint of PB. If `r_(1)` is inradius of PAC and `r_(2)` is ex radius of PBC opposite to P, then `r_(1) + r_(2) =`

Text Solution

Verified by Experts

The correct Answer is:
`((a sqrt3)/(2))`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise PROPERTIES AND SOLUTIONS OF TRIANGLES EXERCISE 7 : SUBJECTIVE TYPE QUESTIONS|18 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise PROPERTIES AND SOLUTIONS OF TRIANGLES EXERCISE 6 : SINGLE INTEGER ANSWER TYPE QUESTIONS|1 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|52 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

Similar Questions

Explore conceptually related problems

In triangle A B C , let /_c=pi/2dot If r is the inradius and R is circumradius of the triangle, then 2(r+R) is equal to

If R be circum-radius of DeltaABC, then circum-radius of a pedal Delta is

P and Q are respectively the midpoints of sides AB and BC or a triangle ABC and R is the mid-point of AP, show ar(RQC) = 3/8 ar(ABC).

P and Q are respectively the midpoints of sides AB and BC or a triangle ABC and R is the mid-point of AP, show ar(PRQ)= 1/2 ar(ARC).

In an equilateral triangle show that the in-radius and the circum-radius are connected by r =R/2.

P and Q are respectively the midpoints of sides AB and BC or a triangle ABC and R is the mid-point of AP, show ar(PBQ)=ar(ARC).

Statement I In a Delta ABC, if a lt b lt c and r is inradius and r_(1) , r_(2) , r_(3) are the exradii opposite to angle A,B,C respectively, then r lt r_(1) lt r_(2) lt r_(3). Statement II For, DeltaABC r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1)=(r_(1)r_(2)r_(3))/(r)

AL, BM and CN are perpendicular from angular points of a triangle ABC on the opposite sides BC, CA and AB respectively. Delta is the area of triangle ABC, (r ) and R are the inradius and circumradius. Radius is the circum circle of Delta LMN is

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

If P,Q and R are the mid-point of the side BC,CA and AB of a triangle and AD is the perpendicular form A and BC, prove that P,Q and D are concylic.

ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (Subjective Type Questions)
  1. In an obtuse angled triangle, the obtuse angle is (3pi)/4 and the othe...

    Text Solution

    |

  2. If in trianlge ABC, a,b,c and angle A are given and c sin A lt a lt c,...

    Text Solution

    |

  3. If P is a point on the altitude AD of the triangle ABC such the /C B P...

    Text Solution

    |

  4. If R denotes circumradius, then in DeltaABC,(b^2-c^2)/(2aR) is equal t...

    Text Solution

    |

  5. In DeltaABC, A = (2pi)/(3), b -c = 3 sqrt3 cm and " area of " Delta AB...

    Text Solution

    |

  6. If Delta = a^(2)-(b-c)^(2), Delta is the area of the Delta ABC then ta...

    Text Solution

    |

  7. In a DeltaABC, B=90^(@), AC=h and the length of perpendicular from B t...

    Text Solution

    |

  8. If in a Delta ABC, sin ^(3) A + sin ^(3) B+ sin ^(3) C =3 sin A .Sin...

    Text Solution

    |

  9. In a triangle ABC, if the sides a,b,c, are roots of x^3-11 x^2+38 x-40...

    Text Solution

    |

  10. If the sides a,b,c are in A.P., prove that (tan)A/2+ (tan) c/2=2/3( co...

    Text Solution

    |

  11. The sides of a triangle are in A.P. and its area is (3)/(5) th of an e...

    Text Solution

    |

  12. If AD, BE and CF are the medians of a Delta ABC, then evaluate (AD^(2)...

    Text Solution

    |

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

    Text Solution

    |

  14. Find the radian measure corresponding to following degree measure 3...

    Text Solution

    |

  15. DeltaABC is equilateral triangle of side a. P lies on AB such that A i...

    Text Solution

    |

  16. The base of a triangle is divided into three equal parts. If theta(1)...

    Text Solution

    |

  17. Find the value of sin ((31pi)/3)

    Text Solution

    |

  18. If the angle at the vertex of an isosceles triangle having the maximum...

    Text Solution

    |

  19. Find the value of trigonometric function sin((5pi)/3)

    Text Solution

    |

  20. Solve cos^2(4x) - cos^2(2x)

    Text Solution

    |