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What is the relationship between an inscribed angle and the central angle that subtends the same arc in a circle?

Study flashcard from the deck Digital SAT Math: Algebra, Advanced Math & Geometry.

Answer

The inscribed angle measures exactly half of the central angle (and half of the intercepted arc measure): $\theta_{\text{inscribed}} = \frac{1}{2} \theta_{\text{central}}$.

Explanation

Consequently, any inscribed angle that intercepts a diameter (a semicircle of $180^\circ$) is a right angle ($90^\circ$, Thales's Theorem).

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