Chapter 10 Circle Theorems and Vocabulary 2024

What is the relationship between a central angle and the corresponding arc on the circle?

They are congruent

What do you use to decide if a line is tangent to a circle?

Pythagorean Theorem

The degree of an inscribed angle is equal to ____ of the measure of its intercepted arc.

half

If you have an inscribed triangle and the diameter is one side of the triangle, then it is a _______________________ triangle.

right

If a quadrilateral is inscribed in a circle, its opposite angles are _________________________.

supplementary (i.e. they add up to 180 degrees)

When two chords in a circle are congruent, what else is congruent?

The two arcs they form.

If two chords intersect inside the circle, then the ____________________ of the lengths of the line segments are equal.

product (a*b = c*d)

Pythagorean Theorem

a²+b² = c²

If two secants intersect outside of a circle, then to find a missing segment, it is...

OUTSIDE*WHOLE=OUTSIDE*WHOLE

A tangent always forms this type of angle with the radius of a circle.

90°

If two tangents meet outside a circle, they have ______________ lengths.

equal or congruent

When two chords meet inside a circle, to find the angle measure you....

add the two arcs and divide by two (find the average)

To find an angle that is outside a circle, you...

subtract the two arcs and divide by two.

secant line

A line that intersects a circle in two points. It goes through the inside of the circle.

tangent line

A line intersects at only one point.

chord

A segment with both endpoints on the circumference of the circle.

diameter

a chord that passes through a center and the other endpoints is on the circle.

Radius

A line segment from the center of the circle to a point on the circle; has half the length of the circle's diameter

To find the diameter of a polygon around circle (created with tangents)

Each tangent piece as a congruent piece across from it. You will double each of those numbers and add for perimeter.

A diameter perpendicular to a chord creates...

Congruent segments and congruent arcs.

When you have a secant and tangent that meet outside the cirlcle, to find a segment length....

outside x whole secant = tangent squared

An angle created by a tangent and chord is...

equal to 1/2 the measure of the intercepted arc

Point of tangency

The point at which a tangent line intersects a circle (example: point D)

Minor Arc

an arc that is smaller then a semi-circle, which means it is smaller than 180 degrees

Major Arc

an arc that is larger than a semi-circle, which means it is bigger than 180 degrees

Equation of a Circle

(x - h)² + (y - k)² = r²

What does (h, k) stand for in the Equation of a Circle?

The Center!

What is the standard form of an equation of a circle if the center is (0, 0)?

x² + y² = r²