Ask Experts Questions for FREE Help !
Ask

    area of isosceles triangle given circle radii

    Asked Dec 20, 2010, 02:49 PM 8 Answers
    Here is a fun little geometry problem. Give it a go if you so desire.

    Look at the graph. The radius of the larger circle is 2r and the radius of the smaller circle is r. Find the area of the triangle.

    There are many ways to go about it. I used simialr triangles, but perhaps you have a better way.

    I just left r=1 in order to graph it. But consider r to be some radius r, not 2 as I have in the graph. The area of the triangle should be expressed in terms of r alone.

    Attached Images Attached Images  
    Search this Question
    Share |
    8 Answers
    ebaines's Avatar
    ebaines Posts: 12,106, Reputation: 1303
    Expert
     
    #2

    Dec 20, 2010, 03:21 PM

    I get:



    Similar triangles seems to be the best way.
    Helpful
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
    Ultra Member
     
    #3

    Dec 20, 2010, 03:33 PM

    Yep. That's it.

    Except, I expressed it as .

    Same thing.

    Cool, ebaines.

    This reminds me of the infinite circles inside the triangle, except it stops at 2 circles. :)
    Helpful
    harum's Avatar
    harum Posts: 339, Reputation: 27
    Full Member
     
    #4

    Dec 20, 2010, 04:46 PM
    Because FE/GD = 2, CG = FG. I.e. CH = 8r. BH = CH * tan(BCH) = CH * (2/sqrt(32)) = CH/sqrt(8) = r*sqrt(8). S = CH*BH = 16*sqrt(8)*r^2.
    Helpful
    harum's Avatar
    harum Posts: 339, Reputation: 27
    Full Member
     
    #5

    Dec 20, 2010, 09:08 PM
    Comment on harum's post
    Quote Originally Posted by harum View Post
    Because FE/GD = 2, CG = FG. I.e. CH = 8r. BH = CH * tan(BCH) = CH * (2/sqrt(32)) = CH/sqrt(8) = r*sqrt(8). S = CH*BH = 16*sqrt(8)*r^2.
    Is there a way to edit a typo? 16*sqrt(2)*r^2
    Helpful
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
    Ultra Member
     
    #6

    Dec 21, 2010, 02:03 AM

    .

    As long as no one else has posted afterwards, I have had no trouble editing a post.

    You meant
    Helpful
    harum's Avatar
    harum Posts: 339, Reputation: 27
    Full Member
     
    #7

    Dec 21, 2010, 02:02 PM
    Comment on galactus's post
    Quote Originally Posted by galactus View Post
    .

    As long as no one else has posted afterwards, I have had no trouble editing a post.

    You meant
    Thanks! 16\sqrt{2}r^{2}
    Helpful
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
    Ultra Member
     
    #8

    Dec 21, 2010, 02:21 PM

    You have to place the tags around your LaTex code.

    Math in brackets at the front and /math in brackets when closing
    Helpful
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
    Uber Member
     
    #9

    Dec 22, 2010, 12:39 PM

    And it may sound weird... but the site has got several 'skins' On the one you are on, harum, you can't edit your own post. It's the 'newer skin' and I personally don't like it. You might try the skin made before that, by looking for your settings and look for something about 'Take me back to the old AMHD' or something along those lines. It's been a while I haven't been there myself.
    Helpful

Not your question? Ask your question View similar questions

 

Question Tools Search this Question
Search this Question:

Advanced Search

Add your answer here.


Check out some similar questions!

Isosceles triangle [ 3 Answers ]

Find the perimeter of an isosceles triangle if the vertex angle measures 50 degrees and the length of the base is 28 cm. help.tnx

Maximum area of a triangle inscribed in a circle, ellipse, conic section [ 1 Answers ]

A triangle inscribed in a circle has to be equilateral triangle for having maximum area ; how? What if it is an ellipse instead of a circle, or a conic section in general ?

Isosceles triangle [ 2 Answers ]

The area of an isosceles triangle is 30 square units.if the base measure 6 units,find the length of the altitude and the ratio of the altitude to the base?

Isosceles triangle [ 1 Answers ]

the sum of the square roots of any two sides of an isoseles triangle is equal to the square root of the remaining side. Is this statement true or false?

Altitude of an Isosceles Triangle [ 1 Answers ]

Ok, find the altitude of an isosceles triangle whose base is 10 and whose congruent sides are 9. I found how to find the alt of a right triangle but still don't really comprende. Help :D


View more questions Search