Results 1 to 5 of 5

Math Help - Area of a triangle

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    18

    Area of a triangle

    This question regards a circle inside a triangle, there are 3 parts to the question and i cannot do any of them but i think if i could do part a) then maybe i could do the rest, if somebody could please help me.

    Q: A right angled triangle with sides a, b and c where a<b<c contains a circle such that the circle just touches all sides of the triangle. The circle has radius of 1cm.

    a) show that ab=a+b+c

    b) show that a+b=c+2

    c)deduce that the area of the triangle is (a+b-1)

    any help would be great, thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Quote Originally Posted by wahhdoe View Post
    This question regards a circle inside a triangle, there are 3 parts to the question and i cannot do any of them but i think if i could do part a) then maybe i could do the rest, if somebody could please help me.

    Q: A right angled triangle with sides a, b and c where a<b<c contains a circle such that the circle just touches all sides of the triangle. The circle has radius of 1cm.

    a) show that ab=a+b+c
    Hi

    The area of the triangle is ab/2
    It is also the sum of the 3 triangles : aR/2 + bR/2 + cR/2 where R is the radius of the circle
    Therefore ab = R(a+b+c)
    And since R=1
    ab = a+b+c

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    18
    ok thanks, the diagram was very useful, it helped me visualize the question which helped alot.

    but even after knowing part a) i am still unable to solve b) and c) would you also be able to help with these parts of the question?

    thanks again for your time
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Nov 2007
    From
    Trumbull Ct
    Posts
    909
    Thanks
    27

    area of a triangle

    Quote Originally Posted by wahhdoe View Post
    This question regards a circle inside a triangle, there are 3 parts to the question and i cannot do any of them but i think if i could do part a) then maybe i could do the rest, if somebody could please help me.

    Q: A right angled triangle with sides a, b and c where a<b<c contains a circle such that the circle just touches all sides of the triangle. The circle has radius of 1cm.

    a) show that ab=a+b+c

    b) show that a+b=c+2

    c)deduce that the area of the triangle is (a+b-1)

    any help would be great, thanks.
    Hi wahhdoe,
    You have part a. I deduce that a,b,c is 3,4,5 and calculate the angle opposite a is 36.8 and its tangent is 3/4. Makes question b and c correct.
    In center radius is 1 and the tangent of 36.8/2 = 1/3

    bjh
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    ab = a+b+c
    a+b = ab-c
    Square both sides
    a+2ab+b = ab-2abc+c
    And since a+b=c
    2ab = ab-2abc
    a and b being not equal to 0 we can divide by ab
    2 = ab - 2c
    But ab = a+b+c
    a+b-c = 2
    a+b = c+2
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Area of Triangle #2
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 8th 2010, 08:19 PM
  2. Replies: 1
    Last Post: October 28th 2008, 07:02 PM
  3. Replies: 7
    Last Post: July 19th 2008, 06:53 AM
  4. The area of a triangle within a triangle
    Posted in the Geometry Forum
    Replies: 4
    Last Post: April 28th 2008, 03:27 AM
  5. Replies: 27
    Last Post: April 27th 2008, 10:36 AM

Search Tags


/mathhelpforum @mathhelpforum