Segment Relationships in Circles:Assessment

Given the figure ,find the value of x.

• 3

• 6

• 9

• 12

Use the figure , if SL = 12 , DL = 18 , and SU = 16, find SB.

• 28.67

• 22.5

• 18

• 12

In the figure , segment BS is tangent to circle T at S. If BC = 8 cm , and CU=10cm, find BS.

• 12

• 14

• 16

• 10

What theorem if two chords intersect in the interior of the circle, then the product of the lengths of the segments of the chord is equal to the product of the lengths of the segments of the other chord.

• The Intersecting Segments of Chords Power Theorem

• The Segments of a Secants Power Theorem

• Arc Length

• The Tangent Secant Segments Power Theorem

Answer explanation

The Intersecting Segments of Chords Power Theorem states that if two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

Given figure 2 at the right, find the measure of segment AL.

• 8

• 9

• 10

• 11

Answer explanation

Segment AL is equal to the sum of segments AK and KL. Given that AK = 4 and KL = 5, AL = 4 + 5 = 9. Therefore, the measure of segment AL is 9.

What is the value of x in figure 5.

• 6

• 36

• 9

• 45

Answer explanation

The value of x in figure 5 is 6 as shown in the diagram.

In figure 6, what is the length of segment GA?

• 6

• 8

• 10

• 12

Answer explanation

In figure 6, segment GA is the hypotenuse of a right triangle with sides of length 6 and 8. Using the Pythagorean theorem (a^2 + b^2 = c^2), GA = sqrt(6^2 + 8^2) = sqrt(36 + 64) = sqrt(100) = 10.

Solve for x.

• A

• B

• C

• D

Answer explanation

The correct answer is D because...

• A
• B
• C
• D

• A
• B
• C
• D