Home
Class 10
MATHS
A circle with centre P is inscribed in t...

A circle with centre P is inscribed in the `triangle` ABC. Side AB, side BC and side AC touch the circle at points L,M and N respectively. Radius of the circle is r. Prove that: `A( triangle ABC)=(1)/(2)(AB+BC+AC)xxr`.

Promotional Banner

Topper's Solved these Questions

  • ARITHMETIC PROGRESSION

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise ASSIGNMENT 3.4|11 Videos
  • BOARD'S QUESTION PAPER : MARCH 2019

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise QUESTION|30 Videos

Similar Questions

Explore conceptually related problems

A circle with centre P is inscribed in the Delta ABC Side AB, side BC and side A C touch the circle at points L,M and N respectively . Prove that : A (DeltaABC ) = 1/2 (AB +BC + AC) xxr

A circle is inscribed in a triangle ABC. It touches the sides AB and AC at M and N respectively. If O is the centre of the circle and angleA = 70^@ , then what is angleMON equal to ?

Delta ABC is an isosceles triangle and AB = AC. If all the sides AB. BC and CA of a Delta ABC touch a circle at D, E and F respectively. Then BE is equal to :

The side AB, BC and CA of triangle ABC touch a circle at P,Q and R respectively. If PA =4 cm, BP=3 cm and AC=11 cm, then length of BC is

The incircle of an isosceles triangle ABC, in which AB = AC, touches the sides BC, CA and AB at D, E and F respectively . Prove that BD = DC.

The sides AB,BC and AC of a triangle ABC touch a circle with centre O and radius r at P Q,and R respectively.

The incircle of an isosceles triangle ABC , with AB=AC , touches the sides AB , BC , CA at D,E and F respectively. Prove that E bisects BC .

In the given figure the sides AB, BE and CA of triangle ABC touch a circle with centre O and radius r at P,Q and R respectively. Prove that : (i) AB+CQ=AC+BQ (ii) Area (triangleABC)=(1)/(2)("Perimeter of"triangleABC)xxr

In triangle ABC,right angled at B, BC = 24 cm, and AB = 7 cm. A circle is inscribed in triangle ABC. Then the radius of the circle is:

NAVNEET PUBLICATION - MAHARASHTRA BOARD-BOARD'S QUESTION PAPER -QUESTION
  1. Out of the following which is a Pythagorean triplet?

    Text Solution

    |

  2. /ACB is inscribed in arc ACB of a circle with centre O . If /ACB= 65^...

    Text Solution

    |

  3. 1+tan^(@)theta =?

    Text Solution

    |

  4. Construct tangent to a circle A and radius 3.4 cm at any point P on it...

    Text Solution

    |

  5. Find slope of a line passing through the points A(3, 1) and B(5, 3).

    Text Solution

    |

  6. Find the surface area of a sphere of radius 3.5 cm.

    Text Solution

    |

  7. In DeltaABC, ray BD bisects /ABC. A-D-C, side DE|| side BC, A-E-B. P...

    Text Solution

    |

  8. Prove that, angles inscribed in the same arc are congruent . Given :...

    Text Solution

    |

  9. How many solid cylinders of radius 6 cm and height 12 cm can by made ...

    Text Solution

    |

  10. In right -angled triangle ABC , BD bot AC . If AD =4 DC =9 then fi...

    Text Solution

    |

  11. Verify whether the following points are collinear or not: A (1, –...

    Text Solution

    |

  12. If sec theta=(25)/(7), then find the value of tan theta

    Text Solution

    |

  13. In DeltaPQR ,seg PM is a median , PM=9 and PQ^(@)+PR^(2)=290. Find th...

    Text Solution

    |

  14. In the figure, O is the centre of circle / QPR = 70^(@) and m (arc PYR...

    Text Solution

    |

  15. Draw a circle with radius 4.2 cm . Construct tangents to the circle fr...

    Text Solution

    |

  16. When an observer at a distance of 12 m from a tree looks at the top of...

    Text Solution

    |

  17. A circle with centre P is inscribed in the triangle ABC. Side AB, side...

    Text Solution

    |

  18. In Delta ABC, angle ACB = 90^(@) ," seg "CD bot side AB and seg CE...

    Text Solution

    |

  19. Show that the points (2,0), (-2,0) and (0,2) are the vertices of a ...

    Text Solution

    |

  20. In the figure, square XLMT is a rectangle. angle M=21 cm, XL = 10. 5 c...

    Text Solution

    |