Angle inscribed in a semicircle

To solve the two problems below you need to know 1) The area of a circle is Πr2, with r as radius and that the area of a semicircle is of course  half of the circle, ½Πrand 2) the angle  in a semicircle theorem.

Problem 1

Prove that the area of the solid green semicircle is equal to the total area of the two smaller semicircles ADC and CGB with diameters AC and CB, respectively.

inscribed triangle

Problem 2

Prove that sum of the area of the two crescents (the area filled with stripes) is equal to the area of the triangle ACB whose vertices are on the green semicircle.

Hint 1: Don’t google for area of crescents.

Hint 2: Answer Problem 1. Do this and you will have the shortest proof ever for Problem 2.

Enjoy these problems with your friends. Email me your answers or better, write them in the comment section.

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