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Math Help - [SOLVED] Triangles and circles

  1. #1
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    [SOLVED] Triangles and circles

    I'm having a problem with a question that involves a circle contained within an equilateral triangle which is also contained by a bigger circle. No sides are given; the question asks to find the ratio between the areas of the two circles. Is there a simple relationship between the two...
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  2. #2
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    Hello orangeiv
    Quote Originally Posted by orangeiv View Post
    I'm having a problem with a question that involves a circle contained within an equilateral triangle which is also contained by a bigger circle. No sides are given; the question asks to find the ratio between the areas of the two circles. Is there a simple relationship between the two...
    Yes - the radius of the circumcircle is twice the radius of the incircle, and its area is therefore 4 times as great. Here's why:

    • Draw a diagram showing an equilateral triangle with its incircle and circumcircle - the two circles you refer to in your question.


    • Draw the three medians of the triangle. They meet at a point, G say, which divides the line joining each vertex of the triangle to the mid-point of the opposite side in the ratio 2:1.

    G is the centre of both circles, and the ratio of their radii is therefore this same ratio 2:1.

    Grandad
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