Given an acute-angled triangle ABC , let points A',B',C' be located as follows: A' i the point where altitude from A on BC meets the outwards-facing semicircle on BC as diameter. Point B',C' are located similarly. Prove that [BC'A']^2 + [CAB']^2 + [ABC']^2 = [ABC]^2
where [ABC] denotes the area of the triangle ABC .
.
.