Math 3 Circles Review

Front

What is the standard equation of a circle?

Back

The standard equation of a circle is (x-h)² + (y-k)² = r², where (h, k) is the center and r is the radius.

Front

How do you find the radius from the circle equation x² + y² - 8x + 10y - 8 = 0?

Back

To find the radius, rewrite the equation in standard form. Completing the square gives the center (4, -5) and radius r = 7.

Front

What is the measure of an angle formed by a tangent and a secant intersecting outside a circle?

Back

The measure of the angle is half the difference of the measures of the intercepted arcs.

Front

If minor arc AC = 72° and minor arc CD = 132°, what is the measure of ∠ ABD?

Back

∠ ABD = 1/2 (132° - 72°) = 30°.

Front

What is the formula to calculate the circumference of a circle?

Back

The circumference C of a circle is given by C = 2πr, where r is the radius.

Front

What is the area of a circle?

Back

The area A of a circle is given by A = πr², where r is the radius.

Front

How do you determine the center of a circle from its equation?

Back

The center (h, k) can be found from the equation (x-h)² + (y-k)² = r².

Front

What is the relationship between the diameter and radius of a circle?

Back

The diameter d is twice the radius: d = 2r.

Front

What is the definition of a tangent line to a circle?

Back

A tangent line touches the circle at exactly one point and is perpendicular to the radius at that point.

Front

What is the definition of a secant line?

Back

A secant line intersects a circle at two points.