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Find each value or measure. Assume all segments that appear to be tangent aretangent. Find US.

Find each value or measure. Assume all segments that appear to be tangent aretangent-example-1

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Intersecting Chords Theorem states that the product of the divided lengths of the line segments on each chord are always equal.

In this case, let's say the intersection of US and RT is O :


(UO)(OS)=(RO)(OT)

Plug in the values of the segments :


(3x+1)(30)=(x+11)(42)

Simplifying the equation :

90x + 30 = 42x + 462

90x - 42x = 462 - 30

48x = 432

x = 9

Substitute x = 9 to US = (3x + 1) + 30

US = [3(9) + 1] + 30

US = 58

The answer is :

US = 58

User Timson
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