Explain how you can use the inscribed angle theorem to justify its second corollary, that an angle inscribed in a semicircle is a right angle.

First, remember that an iscribed angle is an angle, call it α, made from three points on the circumference of the circle.

The inscribed angle theorem states that the  inscribed angle (α) is half of the central angle (2α).

Inscribe a triangle in a semicircle, and you will see that you will have made up the central angle 180°. So the , by the inscribed angle theorem the inscribed angle is half of 180° which is 180°/2 = 90°.

So, always the inscribed angle in a semicircles is 90° which is what a right angle is.

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