Grade 9 Geometry: Secants
This worksheet focuses on understanding and applying properties of secants in circles, including theorems related to angles and segment lengths.
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Grade 9 Geometry: Secants
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. A line that intersects a circle at exactly two points is called a:
Tangent
Chord
Secant
Radius
2. If two secants intersect inside a circle, the product of the segments of one secant is equal to the product of the segments of the other secant. This is known as the:
Tangent-Secant Theorem
Secant-Secant Theorem (Segments)
Chord-Chord Theorem
Inscribed Angle Theorem
3. A secant is a line that intersects a circle at exactly points.
4. When two secants intersect outside a circle, the measure of the angle formed is half the difference of the intercepted arcs.
5. In the circle below, secants AC and AE intersect at point A. If m(arc BC) = 80° and m(arc DE) = 20°, find the measure of angle CAE.
6. Two secant segments are drawn to a circle from an external point P. The segments are PA and PB. If PA = 10, and the external segment of PA is 4, what is the length of the external segment of PB if the entire length of PB is 12?
7. A secant can also be a tangent if it touches the circle at only one point.
True
False
Match the term with its definition:
8. Secant
a. A segment connecting two points on a circle.
9. Chord
b. A line that intersects a circle at exactly two points.
10. Tangent
c. A line that intersects a circle at exactly one point.