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The length of the segment PK of the chord JK in the circle Q is equal to 22
Given that the PQ = QR, it implies that they are at equal distance from the respective chords with which they are perpendicular to so;
LM = JK
9x - 19 = 3x + 23
9x - 3x = 23 + 19 {collect like terms}
6x = 42
x = 42/6
x = 7
JK = 3(7) + 23 = 44
The segment PK = 1/2 × JK
PK = 44/2
PK = 22.
Therefore, the length of the segment PK of the chord JK in the circle Q is equal to 22
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