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Find the value of X.

Find the value of X.-example-1

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Answer:

x = 36

Explanation:

Given a tangent segment of length 24, and a secant segment from the same point with an external length of 12 and a total length of (12+x), you want to find the value of x.

Relation

The product of lengths from the common point to the two intersections with the circle are the same for both segments. In the case of the tangent, the two intersections with the circle are the same point, so the square of the length is used.

24² = 12(12 +x)

2·24 = 12 +x . . . . . . . divide by 12

36 = x . . . . . . . . . subtract 12

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User Braydie
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