Applying the congruent chords theorem, the value of x is: 7.
Length of segment LP is: 6 units.
What is a Chord in Geometry?
In geometry, a chord is defined as the line segment that joins two points on the circumference of a circle.
What is the Congruent Chords Theorem?
In a circle, if two chords are congruent, then they are equidistant from the center of a circle, according to the congruent chords theorem.
In the circle given, chords JK = LM = 12 units. This means both chords are congruent, therefore, they are equidistant from the center of the circle S.
According to the congruent chords theorem, NS = PS, thus:
8 = 2x - 6
8 + 6 = 2x
14 = 2x
Divide both sides by 2
14/2 = 2x/2
7 = x
x = 7
LP = 1/2(12)
LP = 6 units.
In summary, applying the congruent chords theorem, the value of x is: 7.
Length of segment LP is: 6 units.
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