Circle Formulas

Circle Formulas

Formula 1 - Inscribe Angles

Review Formula:

Inscribed Angles are half the size of the Arc's measure in degrees.

Multiple Choice

Inscribed Angles: Find the measure of Arc AB.

• 17

• 34

• 68

• 146

Multiple Choice

Inscribed Angles:

Find the measure of Angle E.

• 7

• 44

• 8

• 50

Formula 2 - Tangent Angles

Related Formula:

The angle formed by a chord and tangent line is half the degrees of the arc.

Multiple Choice

If the minor arc BA measures 148, what is the measure of Angle CBA?

• 74

• 90

• 296

• 32

Formula 3 & 4 - Intersecting Chords

New Formulas:

When two chords intersect, the products of the length of the parts of one chord equal the product of the length of the parts of the other.
When two chords intersect, the resulting interior angle equals the average of the two arcs on either end.

Multiple Choice

Find the value of x.

• 45

• 10

• 20

• 90

Multiple Choice

Solve for x.

Assume that line which appear tangent are tangent.

• 19

• 16

• 13

• 15

Formula 5 & 6 - Tangent & Secant

New Formulas:

The length of the tangent squared is equal to the length of the secant times the part closest to the angle. The angle formed by a tangent and secant is the average difference of the bigger and smaller arc. The angle formula also works with TWO secants so we can call it Secant-Secant

Multiple Choice

Review the steps in the image to solve for X. In addition to the Tangent-Secant formula, what else is needed to solve for X (the length of MN).

• Zero Product Property

• Pythagorean Theorem

• Quadratic Formula

• Inscribed Angle Theorem

Fill in the Blanks

Type the Line or Reason where the error occurs.

Make sure to include the word and number.

Line 1: [(5x + 10) + (3x + 4)]/2 = 30

Reason 1: Secant-Secant Formula

Line 2: [8x + 14]/2 = 30

Reason 2: Combine like terms

Line 3: 4x + 7 = 30

Reason 3: Distributive Property

Line 4: 4x = 23

Line 5: x = 5.75

Reasons 4 and 5: Work backwards with Algebra

Formula 7 - Inscribed Quadrilaterals

Review Formula:

Opposite angles in an inscribed quadrilateral add to make 180. The inscribed angle formula is used to find arc lengths.

Hotspot

Which angles could you solve first with the given information? (Select 2)

Dropdown

If you first solved that angle C was 118, you would next find it's supplement

Select answer

. This angle measures​​

Select answer

. So arc BC is ​

Select answer

, then subtract 59 to find that Arc CD is ​

Select answer

.

Formulas 8 & 9: Sectors & Arc Length

Review Formula:

Usually answers will be simplified fractions when using radians (rather than using 3.14).

Arc Length = (Degrees/180) x (Radius)
Arc Length = (Radians/Pi) x (Radius)

Sector Area = (Degrees/360) x (pi*r²)
Sector Area = (Radians/(2*pi)) x (pi*r²)

Sometimes you need to do Algebra & work backwards to solve for missing radii or angles.

Multiple Choice

The sector's area is 7π and its radius is 4. Solve for radians.

• 7π/8

• 7π/4

• 7π/16

• 7π/2

Multiple Choice

An angle is π/4 radians and a radius is 8. What is the area of the sector formed by the angle?

• 8π

• π

• 64π

• 16π

Math Response

Rearrange the formula to solve for r. You do not need to write "r =" just write what would go after this:

$$a\ =\ \frac{\theta}{180}\left(\pi r\right)$$

Type answer here

Correct Answer: \frac{180a}{\theta\pi}

Deg^°

Rad

Multiple Choice

An angle is 60 degrees and a radius is 6. What is the length of the arc formed by the angle?

• 2π

• π

• 12π

• π/6