Intersecting Chords Lengths

Geometry Circles Review

By Elizabeth Hinds

Intersecting Chords Theorem

Multiple Choice

Solve for x.

• 4

• 6

• 9

• 7

Multiple Choice

Solve for x.

• 10

• 15

• 7.5

• 8

Tangent - Secant Theorem

Multiple Choice

Solve for x.

• 18

• 144

• 12

• 16

Secant-Secant Theorem

Multiple Choice

Solve for x.

• 12

• 1.5

• 1

• 4

Tangent - Tangent Theorem

• Two intersecting tangents are equal to each other

• AB = CB

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.

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.

Two Tangents: angle+arc=180

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

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.

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.

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