Solution

Construct the altitude

hto sidea. Then the area of triangle ABC is

Construct a diameter AQ (it has length 2R) and construct QB. Now ABQ is a right triangle since AQ is a diameter. The angle at Q subtends the chord AB as does the angle at C. Therefore the angles at Q and C have the same measure. Triangle APC is a right triangle and so triangles APC and ABQ are similar.Therefore or .

Substitution gives