SOLVE THIS !
A half-circle is inscribed within an equilateral triangle such that the diameter of the half-circle is centered on one edge of the triangle and the arc is tangent to the other two sides. What is the diameter of the semi-circle if the triangle has an edge length of 4?
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1 solution
We can subtend a line from the tangent of the circle to the midpoint of the base, which is namely the radius. We know the angles are 60 degrees, Hence R=2sin(60) since the tangent is perpendicular namely a right angle triangle. Therefore 2R is the diameter namely 4sin60=2 root 3!