Analyze relationships among inscribed angles, central angles, circumscribed angles, radii, chords, diameters, and tangents.
Use a diameter to conclude an inscribed angle is a right angle
Problem
In this configuration, \(\text{one}~\text{side}\) of an inscribed triangle is a diameter: Triangle \(ABC\) is inscribed in a circle and \(AB\) is a diameter. What can you conclude about the inscribed angle?
A diameter determines a semicircle, but the right angle occurs at the third point on the circle rather than at a diameter endpoint. We’ll identify the inscribed angle intercepting that semicircle and apply the half-arc theorem to locate the right angle.
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