Difference between revisions of "2005 Alabama ARML TST Problems/Problem 3"

Revision as of 17:15, 17 November 2006

Problem

The difference between the areas of the circumcircle and incircle of an equilateral triangle is $\displaystyle 300\pi$ square units. Find the number of units in the length of a side of the triangle.

Solution

Let $R$ be the radius of the circumcircle, and let $r$ be the radius of the incircle. Then we have $R^2-r^2=300$ . But by similarity in the equilateral triangle $r=2r$ , thus $r=10$ ; side length is equal to $10\sqrt{3}$ .

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Difference between revisions of "2005 Alabama ARML TST Problems/Problem 3"

Revision as of 17:15, 17 November 2006

Problem

Solution

Revision as of 13:25, 17 November 2006 (view source) Solafidefarms (talk \| contribs) (awupued)	Revision as of 17:15, 17 November 2006 (view source) JBL (talk \| contribs) m (2005 Alabama ARML TST/Problem 3 moved to 2005 Alabama ARML TST Problems/Problem 3) Newer edit →
(No difference)