Circle Geometry

What is the relationship between a central angle and its intercepted arc?

The measure of a central angle is EQUAL to the measure of its intercepted arc. (m∠Central = mArc)

How do you find the measure of an inscribed angle given its intercepted arc?

An inscribed angle is HALF the measure of its intercepted arc. (m∠Inscribed = 1/2 mArc)

What is the key property of an inscribed quadrilateral's angles?

Its opposite angles are supplementary (add up to 180°).

How do you find the measure of an angle formed by a tangent and a chord?

It's HALF the measure of its intercepted arc.

How do you find the measure of an angle formed by two chords intersecting inside a circle?

It's HALF the SUM of the two intercepted arcs.

How do you find the measure of an angle formed by lines intersecting outside a circle?

It's HALF the DIFFERENCE of the two intercepted arcs (farther arc - closer arc).

What is the relationship between the segments of two chords intersecting inside a circle?

The product of the segments of one chord equals the product of the segments of the other. (Part × Part = Part × Part)

What is the relationship between the segments of two secants drawn from the same external point?

Whole Secant × External Part = Whole Secant × External Part.

What is the relationship between a tangent segment and a secant segment drawn from the same external point?

Tangent² = Whole Secant × External Part.