Answer:
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
