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Secant-Tangent Theorem Worksheet

Explore and apply the Secant-Tangent Theorem to solve for unknown lengths in circles with this Grade 12 math worksheet.

Grade 12 Math GeometrySecant-tangent Theorem
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Includes

Fill in the Blanks3 Short AnswerMultiple ChoiceTrue / False

Standards

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

Topics

GeometryCirclesSecant-Tangent TheoremGrade 12
8 sections · Free to use · Printable
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Secant-Tangent Theorem

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Read each question carefully and apply the Secant-Tangent Theorem to find the unknown lengths. Show all your work.

1. The Secant-Tangent Theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the length of the tangent segment is equal to the product of the length of the   segment and its   segment.

2. In the diagram below, a tangent segment AB and a secant segment AC are drawn to a circle from an exterior point A. If AB = 8 and the external part of the secant, AD = 4, find the length of the entire secant segment AC.

ABCD

3. A tangent segment has a length of 10 units. A secant segment from the same exterior point has an external part of 5 units. Let the internal part of the secant be 'x'. Find the value of x.

4. If a tangent segment is 12 units long and the entire secant segment is 18 units long, what is the length of the external part of the secant segment?

a

6 units

b

8 units

c

10 units

d

12 units

5. The Secant-Tangent Theorem can only be applied when the tangent and secant segments originate from the same external point.

T

True

F

False

6. A point P is outside a circle. A tangent segment from P to the circle is 15 cm long. A secant segment from P intersects the circle at points Q and R, with Q being closer to P. If PQ = 9 cm, find the length of the entire secant segment PR.