I called the radius of circle : . I called the intersection between circle and : . I called the intersection between circle and : . I called the intersection between circle and : . The height of the triangle going through point x: .The points , , and form equilateral triangle . I found line to be . The height of the triangle would be , because the radius of circle is 10, which would make the side length of the triangle . Triangle EPY is a right triangle. So line segment EP would be . So line segment would be , which should equal 15. Solving for , i would get 70/13.5. Equilateral triangle is inscribed in circle , which has radius . Circle with radius is internally tangent to circle at one vertex of . Circles and , both with radius , are internally tangent to circle at the other two vertices of . Circles , , and are all externally tangent to circle , which has radius , where and are relatively prime positive integers. Find .
A alternate solution I came up with was to use triangle .I know angle is 60 degrees. So using the cosine law, I would get: which also comes out to = 70/13.
However my answer is wrong. The correct answer is 27/5. Could someone tell me what I am doing wrong? Thank you.
*I am sorry if i posted this in the wrong section. This is mostly geometry, but there is a bit of trig at the end.