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Circle theorems

Jessica White

Jessica White

7 min read

Study Guide Overview

This study guide covers circle theorems relevant to the SAT Math section, including central, inscribed, and circumscribed angles, as well as tangent-chord angles and cyclic quadrilaterals. It also explains chord properties, secant and tangent relationships, and related theorems with formulas. The guide provides practice questions and emphasizes important test-taking strategies.

Circle Theorems: Your Ultimate Guide for the SAT Math 🎯

Hey there! Let's dive into the world of circles. These theorems are super important for the SAT, and once you get the hang of them, you'll be solving problems like a pro! This guide is designed to be your go-to resource the night before the exam. Let's make sure you're feeling confident and ready to ace it!

Angles in Circles

Central and Inscribed Angles

Key Concept

These two types of angles are the foundation for many circle problems. Understanding their relationship with intercepted arcs is key.

  • Central Angle:

    • Formed by two radii meeting at the circle's center.
    • Its measure is equal to the measure of its intercepted arc. Think of it like a direct match! 📐

    Central Angle

  • Inscribed Angle:

    • Formed by two chords that meet on the circle's circumference.
    • Its measure is half the measure of its intercepted arc (or half the central angle that intercepts the same arc). It's like the central angle is sharing its measure. 🤓

    Inscribed Angle

  • Inscribed Angle Theorem:

    • Inscribed angles that intercept the same arc are congruent (equal). If they're looking at the same slice of the pie, they're the same angle! 👯
  • Angles in a Semicircle:

    • An angle inscribed in a semicircle is always a right angle (90 degrees). This is a classic setup on the test. 📐
Memory Aid

Think of the central angle as the "king" of the arc – it gets the full measure. The inscribed angle is like the "prince" – it gets half the measure.

Special Angle Relationships

  • Circumscribed Angle:
    • Formed by two tangent lines...

Question 1 of 11

If a central angle in a circle measures 80 degrees, what is the measure of the inscribed angle that intercepts the same arc? 🤔

40 degrees

80 degrees

160 degrees

20 degrees