# 10-5 Segment Relationships in Circles Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

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• 10-5Segment Relationships in CirclesHolt GeometryWarm UpLesson PresentationLesson Quiz

• 4481410.5 Segment Relationships in Circles

• Find the lengths of segments formed by lines that intersect circles.

Use the lengths of segments in circles to solve problems.Objectives10.5 Segment Relationships in Circles

• secant segmentexternal secant segmenttangent segment

Vocabulary10.5 Segment Relationships in Circles

• In 1901, divers near the Greek island of Antikythera discovered several fragments of ancient items. Using the mathematics of circles, scientists were able to calculate the diameters of the complete disks.

The following theorem describes the relationship among the four segments that are formed when two chords intersect in the interior of a circle.10.5 Segment Relationships in Circles

• 10.5 Segment Relationships in Circles

• Example 1: Applying the Chord-Chord Product TheoremFind the value of x and the length of each chord.10(7)= 14(x)70 = 14x5 = xEF = 10 + 7 = 17GH = 14 + 5 = 1910.5 Segment Relationships in Circles

EJ JF = GJ JH

• Check It Out! Example 1 Find the value of x and the length of each chord.8(x) = 6(5)8x = 30x = 3.75AB = 6 + 5 = 11CD = 3.75 + 8 = 11.7510.5 Segment Relationships in Circles

DE EC = AE EB

• Example 2: Art ApplicationThe art department is contracted to construct a wooden moon for a play. One of the artists creates a sketch of what it needs to look like by drawing a chord and its perpendicular bisector. Find the diameter of the circle used to draw the outer edge of the moon.10.5 Segment Relationships in Circles

• Example 2 Continued8d = 1458d 64 = 818 (d 8) = 9 910.5 Segment Relationships in Circles

• Check It Out! Example 2 What if? Suppose the length of chord AB that the archeologists drew was 12 in. In this case how much longer is the disks diameter compared to the disk on p. 793?6(6) = 3(QR)12 = QR12 + 3 = 15 = PR10.5 Segment Relationships in Circles

AQ QB = PQ QR

• A secant segment is a segment of a secant with at least one endpoint on the circle. An external secant segment is a secant segment that lies in the exterior of the circle with one endpoint on the circle.10.5 Segment Relationships in Circles

• 10.5 Segment Relationships in Circles

• Find the value of x and the length of each secant segment.Example 3: Applying the Secant-Secant Product Theorem112 = 64 + 8x48 = 8x6 = xED = 7 + 9 = 16EG = 8 + 6 = 1410.5 Segment Relationships in Circles

16(7) = (8 + x)8

• Check It Out! Example 3 Find the value of z and the length of each secant segment.351 = 169 + 13z182 = 13z14 = zLG = 30 + 9 = 39JG = 14 + 13 = 2710.5 Segment Relationships in Circles

39(9) = (13 + z)13

• 10.5 Segment Relationships in Circles

• 10.5 Segment Relationships in Circles

• Example 4: Applying the Secant-Tangent Product TheoremFind the value of x.The value of x must be 10 since it represents a length.ML JL = KL220(5) = x2100 = x210 = x10.5 Segment Relationships in Circles

• Check It Out! Example 4 Find the value of y.DE DF = DG27(7 + y) = 10249 + 7y = 1007y = 5110.5 Segment Relationships in Circles

• Lesson Quiz: Part I1. Find the value of d and the length of each chord.d = 9ZV = 17WY = 182. Find the diameter of the plate.10.5 Segment Relationships in Circles

• Lesson Quiz: Part IIx = 10QP = 8QR = 124. Find the value of a.83. Find the value of x and the length of each secant segment.10.5 Segment Relationships in Circles

• Video1. Find the value of x and the length of each secant segment.10.5 Segment Relationships in Circles

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