Geometry Circle Angles and Lengths

Geometry Circles Review

By Elizabeth Hinds

Intersecting Chords Theorem

Multiple Choice

Solve for x.

• 4

• 6

• 9

• 7

Fill in the Blank

Solve for x

Multiple Choice

Solve for x.

• 10

• 15

• 7.5

• 8

Tangent - Secant Theorem

Multiple Choice

Solve for x.

• 18

• 144

• 12

• 16

Fill in the Blank

Solve for x.

Secant-Secant Theorem

Multiple Choice

Solve for x.

• 12

• 1.5

• 1

• 4

Fill in the Blank

Solve for x

Tangent - Tangent Theorem

• Two intersecting tangents are equal to each other

• AB = CB

Fill in the Blank

Solve for x.

Central angle: angle=arc

Central angles have a vertex at the center of the circle. The arc created by the two radii is equal to the angle.

Fill in the Blank

What is x?

Inscribed Angle: angle=1/2*arc or arc=2*angle

Inscribed angles must have a vertex touching the circle. The angle is half of the outside arc or the arc is twice the angle inside.

Fill in the Blank

What is x?

Two Tangents: angle+arc=180

Two tangents create an angle and an arc (small arc). These two added together always equal 180.

Fill in the Blank

What is x equal to?

External: angle=1/2(big arc - little arc)

When two secants meet outside of a circle, the angle is equal to half of the different of the arcs.

Fill in the Blank

What is the measure of the missing angle?

Internal: angle=1/2(big arc + little arc)

When two secants meet inside the circle, the angle is equal to half of the sum of the arcs.

Fill in the Blank

What is the measure of the internal angle?

Inscribed Quadrilateral: opposite angles =180

When a quadrilateral is inscribed in a circle, the opposite angles always add to 180.

Multiple Select

Select all equations that can be used to solve for x and y in the following inscribed quadrilateral.

• x+55=180

• y+85=180

• x+85=180

• y+55=180

From the Equation

• Make the signs on h and k OPPOSITE to get the center

• Take the SQUARE ROOT of r² to get the radius

• If you don't SEE a h or k, then that means the coordinate is ZERO.

Multiple Choice

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

• (3,2)

• (-3, -2)

• (-2, -3)

• (2, 3)

Multiple Choice

In the equation (x-3)²+(y-2)²=16, the radius of the circle is...

• 16

• 32

• 8

• 4

Multiple Choice

In the equation x²+(y+5)²=10, what is the center?

• (1, 5)

• (-1, -5)

• (0, 5)

• (0, -5)

Multiple Choice

The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.

• (x - 2)² + (y + 5)² = 36

• (x - 5)² + (y + 2)² = 6

• (x + 5)² + (y - 2)² = 36

• (x + 2)² + (y - 5)² = 6

Multiple Choice

Write the equation of a circle with center (7, 0) with radius 3.

• (x - 7)² + y² = 9

• x² + (y -7)² = 9

• (x - 7)² + y² = 3

• x² + (y -7)² = 3

Multiple Choice

What is the equation for this circle?

• (x+1)²+(y+1)²=9

• x²+y²=9

• x²+y²=6

• x²+y²=3

Multiple Choice

What is the equation of the circle?

• (x+1)² + (y +1)² = 3

• (x+1)² + (y -1)² = 3

• (x+1)² + (y +1)² = 9

• (x-1)² + (y -1)² = 9