Based on the two-secants theorem, the length of FG is approximately 20.3 units.
What is the Two-Secants Theorem?
The two-secants theorem states that when two secants intersect each other at a point outside a circle, product of the secant segment and its external portion would be equal to the product of the second secant segment and its external portion in the given circle.
Given the following:
IH = 29
JI = 23
GH = 30
FG = ?
Based on the two-secants theorem, we have:
GH × FH = IH × JH
Substitute
30 × (30 + FG) = 29 × (29 + 23)
900 + 30(FG) = 1,508
900 + 30(FG) - 900 = 1,508 - 900
30(FG) = 608
30(FG)/30 = 608/30
FG ≈ 20.3 units.
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