Home
Class 10
MATHS
In the given figure the sides AB, BE and...

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`

Text Solution

Verified by Experts

The correct Answer is:
19cm
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • CIRCLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Long Answer Questions|2 Videos

  • CIRCLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Short Answer Questions|4 Videos

  • ARITHMETIC PROGRESSION

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Long Answer Question|5 Videos

  • CO-ORDINATE GEOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Short Answer Questions|10 Videos

Similar Questions

Explore conceptually related problems

In Fig. 10.20, the sides A B ,\ B C and C A of triangle A B C touch a circle with centre O and radius r at P ,\ Q and R respectively. (FIGURE) Prove that: 1) AB + CQ = AC + BQ

In Fig.2, a quadrilateral ABCD is drawn to circumscribe a circle, with centre O, in such a way that the sides AB, BC, CD and DA touch the circle at the points P, Q, R and S respectively. Prove that AB + CD = BC + DA.

Knowledge Check

  • In a triangle ABC, the incircle (centre O) touches BC , CA and AB at points P,Q and R respectively. Calculate: (i) /_QOR (ii) /_QPR given that /_A=60^(@)

    A
    (i) `120^(@)` (ii) `60^(@)`
    B
    (i) `110^(@)` (ii) `50^(@)`
    C
    (i) `145^(@)` (ii) `80^(@)`
    D
    (i) `90^(@)` (ii) `40^(@)`

    • Similar Questions

    Explore conceptually related problems

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

    The sides AB and AC of a triangle ABC are produced, and the bisectors of the external angles at B and C meet at P. Prove that if AB gt AC , then PC gt PB .

    A circle is touching the side BC of a triangle ABC at point P and touching AB and AC produced at Q and R respectively. Prove that AQ=(1)/(2)("perimeter of "triangle ABC).

    In the given figure ABC is a triangle and BC is parallel to the Y-axis. AB and AC intersects the y-axis at Pand Q respectively. (i) Write the coordinates of A.

    In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC and AC at points D, E and F respectively. If AB= 12 cm, BC= 8 cm and AC = 10 cm, find the lengths of AD, BE and CF.

    In the figure, given, ABC is a triangle and BC is parallel to the y-axis. AB and AC intersect the y-axis at P and Q respectively. Find the length of AB and AC.

    AB is the diameter of a circle with centre O. A line PQ touches the given circle at point R and cuts the tangents to the circle through A and B at points P and Q respectively. Prove that /_POQ=90^(@)

    Home
    Profile