Use circle angle relationships (central/inscribed angles; chords/tangents) when relevant. | Circles | SAT Math

Central angles equal their intercepted arcs, and inscribed angles are half the same arc. A diameter always creates a right inscribed angle.

Core Idea

A central angle equals the arc it intercepts. An inscribed angle is half the intercepted arc. When both intercept the same arc, the inscribed angle is half the central angle.

Understanding

Rule: Central and inscribed angles follow different rules.

A central angle equals its intercepted arc.
An inscribed angle is half its intercepted arc.
If they intercept the same arc, the inscribed angle is half the central angle.

A diameter creates a semicircle, so the inscribed angle there is $90 \circ$ .

Step by Step

Determine whether the angle is central (vertex at center) or inscribed (vertex on the circle).
If central: angle = arc.
If inscribed: angle = $12$ × arc.
If both share the same arc, the inscribed angle is half the central angle.

Misconceptions

Applying the inscribed angle rule to a central angle (or vice versa).
Thinking the inscribed angle is half the central angle in all cases — only when they intercept the same arc.
Forgetting the semicircle rule: inscribed angle on a diameter is 90°.

Question

Worked Example

A central angle in a circle measures 110°. An inscribed angle intercepts the same arc. What is the measure of the inscribed angle?

Select an answer to see the explanation