Off on a Tangent – Summative Assessment
Name: _______________________________________ Date: _______________ Period: ____
Directions: Determine if each statement is TRUE or FALSE and write your answer here .
1. The diameter of a circle passes through the center of the circle.
1. __________
2. A chord is a segment on a secant line.
2. __________
3. A chord is a segment on a tangent line.
3. __________
4. A chord is a radius.
4. __________
5. The diameter of a circle is equal to half the radius of the circle.
5. __________
6. All radii have the center of the circle as an endpoint.
6. __________
7. The diameter is the longest chord in a circle.
7. __________
8. A tangent line may intersect the circle at more than one point.
8. __________
9. A secant line may intersect the circle at more than one point.
9. __________
10. A point of tangency lies on the circumference of a circle.
10. _________
11. All diameters have the center of the circle as an endpoint.
11. _________
12. There is only one tangent line to a circle from a point outside the circle.
12. _________
13. Diameter is the product of two and the radius.
13. _________
14. The measure of arc AB equals the measure of segment AB.
14. _________
15. Chords are always in the exterior of a circle.
15. _________
16. Tangent lines are always in the interior of a circle.
16. _________
17. A point on the circumference of a circle is also in the exterior of the circle.
17. _________
18. A radius is a chord.
18. _________
19. A diameter is a chord.
19. _________
20. A point of tangency is a vertex of an acute angle formed by a radius and a
tangent line.
20. _________
21. Tangent lines and secant lines to a circle are always parallel to each other.
21. _________
Off on a Tangent – Summative Assessment (Answer Key)
Name: _______________________________________ Date: _______________ Period: ____
Directions: Determine if each statement is TRUE or FALSE and write your answer here .
1. The diameter of a circle passes through the center of the circle.
1. __TRUE__
2. A chord is a segment on a secant line.
2. __TRUE__
3. A chord is a segment on a tangent line.
3. __FALSE_
4. A chord is a radius.
4. __FALSE_
5. The diameter of a circle is equal to half the radius of the circle.
5. __FALSE_
6. All radii have the center of the circle as an endpoint.
6. __TRUE__
7. The diameter is the longest chord in a circle.
7. __TRUE__
8. A tangent line may intersect the circle at more than one point.
8. __FALSE_
9. A secant line may intersect the circle at more than one point.
9. __TRUE__
10. A point of tangency lies on the circumference of a circle.
10. _TRUE__
11. All diameters have the center of the circle as an endpoint.
11. _FALSE_
12. There is only one tangent line to a circle from a point outside the circle.
12. _FALSE_
13. Diameter is the product of two and the radius.
13. _TRUE__
14. The measure of arc AB equals the measure of segment AB.
14. _FALSE_
15. Chords are always in the exterior of a circle.
15. _FALSE_
16. Tangent lines are always in the interior of a circle.
16. _FALSE_
17. A point on the circumference of a circle is also in the exterior of the circle.
17. _FALSE_
18. A radius is a chord.
18. _FALSE_
19. A diameter is a chord.
19. _TRUE__
20. A point of tangency is a vertex of an acute angle formed by a radius and a
tangent line.
20. _FALSE_
21. Tangent lines and secant lines to a circle are always parallel to each other.
21. _FALSE_
Off on a Tangent – Summative Assessment
22. Name the two geometric construction tools necessary to construct a tangent line from a point
outside a given circle to the circle. _____________________ and _____________________
23. Steps that describe how to construct a tangent line from a point outside a given circle to the
circle are listed below. Arrange them from first (1) to last (4) by writing letters on the lines.
A. Find the midpoint of the line segment
B. Strike an arc across the circle to determine the points of tangency
C. Draw a line segment connecting the circle’s center and the given point
D. Draw the tangent line through the points of tangency and the given point
1. ________
2.________
3._________ 4.________
24. How does the distance a given point outside a circle is from the circle affect the tangent lines
to the circle, if at all?
25. Explain why the two tangent lines to a circle from a point outside the circle will never be
perpendicular to the same diameter.
26. Discuss the presence of reflective symmetry within the process of constructing a tangent line
to a circle from a point outside the circle.
Off on a Tangent – Summative Assessment (Answer Key)
22. Name the two geometric construction tools necessary to construct a tangent line from a point
outside a given circle to the circle. _____compass_________ and ____straightedge______
23. Steps that describe how to construct a tangent line from a point outside a given circle to the
circle are listed below. Arrange them from first (1) to last (4) by writing letters on the lines.
A. Find the midpoint of the line segment
B. Strike an arc across the circle to determine the points of tangency
C. Draw a line segment connecting the circle’s center and the given point
D. Draw the tangent line through the points of tangency and the given point
1. ____C___ 2.____A___
3.____B____ 4.____D___
24. How does the distance a given point outside a circle is from the circle affect the tangent lines
to the circle, if at all? Regardless of the distance, there will always be two tangent lines.
25. Explain why the two tangent lines to a circle from a point outside the circle will never be
perpendicular to the same diameter. The two tangent lines to a circle through a point not
on the circle will always pass through the point outside the circle and thus intersect.
By definition, intersecting lines are not parallel. The chord with endpoints at the two
corresponding points of tangency on the circle will never be a diameter.
26. Discuss the presence of reflective symmetry within the process of constructing a tangent line
to a circle from a point outside the circle. There are two instances of reflective symmetry,
the center of the circle and the given point outside the circle are reflections over the
midpoint of the line segment connecting them, and the two points of tangency on the
circle are reflections over the previously mentioned line segment.