Problem

Problem

In an acute angled ΔABC\Delta ABC , the points A′,B′A', B' and C′C' are located such that A′A' is the point where altitude from AA on BCBC meets the outward facing semi-circle drawn on BCBC as diameter, points B′,C′B', C' are located similarly. Prove that {ar(BCA′)}2+{ar(CAB′)}2+{ar(ABC′)}2={ar(ABC)}2\{\text{ar}(BCA')\}^2 + \{\text{ar}(CAB')\}^2 + \{\text{ar}(ABC')\}^2 = \{\text{ar}(ABC)\}^2

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