Secants in Circles Worksheet

Explore the properties of secant lines and their relationships with circles, including theorems related to segments and angles formed by secants.

Grade 12 Math GeometrySecants

Use This Worksheet

Includes

3 Short AnswerMultiple ChoiceFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.HSG.C.A.2CCSS.MATH.CONTENT.HSG.C.A.3

Topics

geometrycirclessecantstheoremsgrade12

8 sections · Free to use · Printable

← More Math worksheets for Grade 12

Secants in Circles Worksheet

Name:

Date:

Score:

Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. Define a secant line in the context of a circle. How does it differ from a tangent line?

2. If two secants intersect outside a circle, which of the following relationships is true?

Part * Whole = Part * Whole

Arc Angle = 1/2 (Intercepted Arc)

Angle = 1/2 (Far Arc - Near Arc)

Angle = 1/2 (Sum of Intercepted Arcs)

3. The theorem that describes the relationship between the segments of two secants intersecting outside a circle states that the product of the of one secant segment and its segment is equal to the product of the of the other secant segment and its segment.

4. When two secants intersect inside a circle, the measure of the angle formed is one-half the of the measures of the arcs.

5. In the circle below, secant segments PA and PB are drawn from an external point P. If PA = 8 and PC = 3 (where C is on the circle such that P-C-A), and PB = x and PD = 4 (where D is on the circle such that P-D-B), find the value of x.

6. A secant line can intersect a circle at exactly one point.

True

False

7. The angle formed by two secants intersecting inside a circle is always an acute angle.

True

False

8. Two secant segments are drawn to a circle from an external point. The external segment of the first secant is 5 units, and its whole length is 12 units. If the whole length of the second secant is 15 units, what is the length of its external segment?