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`.

Answer

Step by step text solution for 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. by MATHS experts to help you in doubts & scoring excellent marks in Class 10 exams.

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • BOARD QUESTION PAPER: MARCH 2019

    TARGET PUBLICATION|Exercise (Solve the following questions (Any three):|4 Videos

  • ARITHMETIC PROGRESSION

    TARGET PUBLICATION|Exercise Chapter Assessment|17 Videos

  • CHALLENGING QUESTIONS

    TARGET PUBLICATION|Exercise Chapter 6: Statistics|4 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 ?

Knowledge Check

  • A circle is inscribed in a triangle ABC. It touches the sides AB, BC and AC at the points R, P and Q respectively. If AQ = 4.5 cm, PC = 5.5 cm and BR = 6 cm, then the perimeter of the triangle ABC is:

    A
    `30.5 cm`.
    B
    `28 cm`.
    C
    `32 cm`.
    D
    `26.5 cm`.

  • 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 :

    A
    `(1)/(2)` BC
    B
    `(1)/(3)` BC
    C
    `(1)/(4)` BC
    D
    `(2)/(3)` BC

    • Similar Questions

    Explore conceptually related problems

    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:

    Home
    Profile