Math 3 Circles Test Unit 6

Front

What is the measure of arc TW if it is given that the measure is 41 degrees?

Back

The measure of arc TW is 41 degrees.

Front

How do you find the value of x in the equation DE = 5x + 6 and FG = 11x - 72?

Back

To find x, set the two expressions equal: 5x + 6 = 11x - 72. Solving gives x = 13.

Front

What is the formula for the circumference of a circle?

Back

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

Front

If the length of the 45° region of a circle is 10 inches, how do you find the radius?

Back

Use the formula for arc length: L = (θ/360) * 2πr. Rearranging gives r = (L * 360) / (θ * 2π). For θ = 45°, r = 12.76 inches.

Front

What is the standard form of a circle's equation?

Back

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

Front

How do you convert the equation x² + y² + 4x + 6y - 36 = 0 to standard form?

Back

Complete the square for x and y: (x + 2)² + (y + 3)² = 49.

Front

What is the relationship between the angles and arcs in a circle?

Back

The measure of an arc is directly proportional to the angle subtended at the center of the circle.

Front

What is the formula for 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 find the length of an arc given the radius and angle?

Back

Use the formula L = (θ/360) * 2πr, where θ is the angle in degrees.

Front

What is the definition of a chord in a circle?

Back

A chord is a line segment with both endpoints on the circle.