You've explored how various rules about the relationships among a circle's parts can help you find missing information about a circle. For this activity, you'll need to decide which rules or relationships can help you solve the problem—and then solve it. Choose the correct answer for each problem and read the feedback carefully. These questions are similar to the ones you'll see on the lesson quiz.
1. Find the value of x in this circle.
- 12.0
- 8.6
- 23.1
- 4.2
Two chords intersect inside the circle. 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.
14x = 20(6), so x = 8.6.
Two chords intersect inside the circle. 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.
Two chords intersect inside the circle. 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.
2. In the following diagram, identify a chord.
- \(\small\mathsf{ \overline {LG}}\)
- \(\small\mathsf{ \overline {JC}}\)
- \(\small\mathsf{ \overleftrightarrow {GH}}\)
- \(\small\mathsf{ \overline {CL}}\)
\(\small\mathsf{ \overline {LG}}\) is a chord because its endpoints are on the circle. \(\small\mathsf{ \overline {GH}}\) would be a chord, but \(\small\mathsf{ \overleftrightarrow {GH}}\) is a secant.
A chord is a segment whose endpoints are on the circle.
A chord is a segment whose endpoints are on the circle.
A chord is a segment whose endpoints are on the circle.
3. In the following diagram, identify a radius.
- \(\small\mathsf{ \overline {LG}}\)
- \(\small\mathsf{ \overline {JC}}\)
- \(\small\mathsf{ \overleftrightarrow {GH}}\)
- \(\small\mathsf{ \overline {LH}}\)
A radius is a segment with one endpoint on the circle and the other endpoint is the center of the circle.
A radius is a segment with one endpoint on the circle and the other endpoint is the center of the circle.
A radius is a segment with one endpoint on the circle and the other endpoint is the center of the circle.
\(\small\mathsf{ \overline {CL}}\) is a radius because it has one endpoint that is on the circle (point L) and the other endpoint (point C) is the center of the circle.
4. In the following diagram, identify a tangent.
- \(\small\mathsf{ \overleftrightarrow {JM}}\)
- \(\small\mathsf{ \overline {CJ}}\)
- \(\small\mathsf{ \overleftrightarrow {GH}}\)
- \(\small\mathsf{ \overline {CH}}\)
\(\small\mathsf{ \overleftrightarrow {JM}}\) is a tangent because it is a line that intersects the circle at one point.
A tangent is a line that intersects the circle in exactly one point.
A tangent is a line that intersects the circle in exactly one point.
A tangent is a line that intersects the circle in exactly one point.
5. Find the value of the variable in this diagram.
- 5.0
- 6.4
- 1.4
- 12.6
The product of the two segments of one chord is equal to the product of the two segments of the other chord.
The product of the two segments of one chord is equal to the product of the two segments of the other chord. 14x = 10(9), 14x = 90, x = \(\small\mathsf{ \frac {90} {14} }\) = 6.4
The product of the two segments of one chord is equal to the product of the two segments of the other chord.
The product of the two segments of one chord is equal to the product of the two segments of the other chord.
6. Find the value of the variable.
- 7
- 15
- 1.875
- 20.125
This image shows segments formed by a tangent and a secant. To find a missing segment, you multiply the exterior segment by the whole segment.
This image shows segments formed by a tangent and a secant. To find a missing segment, you multiply the exterior segment by the whole segment.
This image shows segments formed by a tangent and a secant. To find a missing segment, you multiply the exterior segment by the whole segment.
This image shows segments formed by a tangent and a secant. To find a missing segment, you multiply the exterior segment by the whole segment.
8(8+x) = 15²
64 + 8x = 225
8x = 161
x = 20.125
7. Find the value of the variable.
- 21
- 28
- 18
- 24
The segments are formed by two intersecting secants. To find a missing segment, you multiply the exterior segment by the whole segment.
The segments are formed by two intersecting secants. To find a missing segment, you multiply the exterior segment by the whole segment.
The segments are formed by two intersecting secants. To find a missing segment, you multiply the exterior segment by the whole segment.
The segments are formed by two intersecting secants. To find a missing segment, you multiply the exterior segment by the whole segment.
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