The value of x is 4.
What is the intersecting chords theorem?
The chord theorem is defined as a statement in basic geometry that explains the relationship between the four line segments formed by two intersecting chords inside of a circle. According to this statement, the products of the line segment lengths on each chord are equal. It is also known as the intersecting chords theorem.
According to given figure,
TW = 3,
CW = x,
VW = 6,
Chord TU = x + 7,
WU = TU - TW
Substitute the value of Chord TU in above equation,
WU = x + 7 - 3
WU = x + 4
According to property of intersecting chords inside a circle, the products of the line segment lengths on each chord are equal.
TW × WU = VW × CW
3(x + 4) = 6 × x
3x + 12 = 6x
12 = 6x - 3x
12 = 3x
x = 12/3
x = 4
Hence, the value of x is 4.
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