Lesson 3 Circles Segment Theorems ppt 2: Exit Ticket
01.

1. x = 7.25

2. x = 36

Explanation:

1. Base on intersecting secants theorem, therefore:

DE × DF = DG × DH

DE = 11

DF = 11 + 10 = 21

DG = 12

DH = 12 + x

Therefore,

11*21 = 12(12 + x)

231 = 144 + 12x

231 - 144 = 12x

87 = 12x

Divide both sides by 12

x = 7.25

2. Based on the secant-tangent rule, we have:

CD*CA = CB²

CD = 12

CA = 12 + x

CB = 24

Thus:

12(12 + x) = 24²

144 + 12x = 576

12x = 576 - 144

12x = 432

Divide both sides by 12

x = 432/12

x = 36

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