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- Apr 14, 2013

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We have a rectangle inside a semicircle with radius $1$ :

From the midpoint of the one side we draw a line to the opposite vertices and one line to the opposite edge.

Are the acute angles of the right triangles all equal to $45^{\circ}$ ?

All four triangles are similar, aren't they? We have that the hypotenuse of each right triangle is equal to $1$, since it is equal to the radius of the circle.

I am stuck right now about the angles.