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10-7 Study Guide and Intervention
Special Segments in a Circle
Segments Intersecting Inside a Circle If two chords intersect in a circle,
then the products of the lengths of the chord segments are equal.
a ⋅ b = c ⋅ d
Example: Find x.
The two chords intersect inside the circle, so the products AB ⋅ BC and EB ⋅ BD are equal.
AB ⋅ BC = EB ⋅ BD
6 ⋅ x = 8 ⋅ 3 Substitution
6x = 24 Multiply.
x = 4 Divide each side by 6. AB ⋅ BC = EB ⋅ BD
Exercises
Find x. Assume that segments that appear to be tangent are tangent. Round to the nearest tenth if necessary.
1. 2.
3. 4.
5. 6.
7. 8.
10-7 Study Guide and Intervention (continued)
Special Segments in a Circle
Segments Intersecting Outside a Circle If secants and tangents intersect outside a circle, then two products are equal. A secant segment is a segment of a secant line that has exactly one endpoint on the circle. A secant segment that lies in the exterior of the circle is called an external secant segment. A tangent segment is a segment of a tangent with one endpoint on the circle.
Chapter 10 44 Glencoe Geometry
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• If two secants are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.
AC and AE are secant segments.
AB and AD are external secant segments.
AC ⋅ AB = AE ⋅ AD
• If a tangent segment and a secant segment are drawn to a circle from exterior point, then the square of the measure of the tangent segment is equal to the product of the measures the secant segment and its external secant segment.
AB is a tangent segment.
AD is a secant segment.
AC is an external secant segment.
(AB)2 = AD ⋅ AC
Chapter 10 44 Glencoe Geometry
NAME DATE PERIOD
Example: AB is tangent to the circle. Find x. Round to the nearest tenth.
The tangent segment is AB, the secant segment is BD, and the external
secant segment is BC.
(AB)2 = BC ⋅ BD
(18)2 = 15(15 + x) Substitution.
324 = 225 + 15x Multiply.
99 = 15x Subtract 225 from both sides.
6.6 = x Divide both sides by 15.
Exercises
Find x. Round to the nearest tenth. Assume segments that appear to be tangent are tangent.
1. 2. 3.
4. 5. 6.
Chapter 10 44 Glencoe Geometry