Geometry Problem 1443: Triangle Area, Incenter, Circumcenter, 90 Degree, Perpendicular, One-third Measurement

I and O are the incenter and circumcenter of a triangle ABC so that the measure of the angle BIO is 90 degree. Prove that the area of the triangle AIC is one-third the area of the triangle ABC.

See solution below

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Poster of Problem 1443 using iPad Apps

Poster of Problem 1443 using iPad Apps

See also:
Art of problem 1442, Generative Sketching.

Geometric Art using iPad or Mobile Apps

Geometric art is a form of art based on the use and application of geometric figures. A geometric figure is any set or combination of points, lines, surfaces and solids.

A mobile app or mobile application software is a computer program designed to run on smartphones and tablet computers.