知识点 4

Work with circles (arcs, chords, tangents, central/inscribed angles) and circle equations when presented.

Circle questions usually come down to arc, radius, or standard-form relationships.

核心知识

In circle problems, connect everything to the intercepted arc or a radius fact: a central angle equals its arc, an inscribed angle is half its intercepted arc, and a tangent is perpendicular to the radius at the point of tangency.

深入理解

Rule: Circle questions become simpler when you ask what arc or radius relationship controls the picture. Central angles match their arcs directly. Inscribed angles are half the intercepted arc. Equal chords subtend equal arcs, and tangent segments create right angles with radii at the point of tangency.

If ACT gives a circle equation, standard form lets you read the center and radius directly instead of expanding anything.

题目

示例解析

A central angle intercepting arc 𝐴𝐵 measures 110. What is the measure of an inscribed angle intercepting the same arc 𝐴𝐵?

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