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In the following picture, (QS) ̅ and (PR) ̅ are chords of the circle. Find the length of QS. (Remember to show formulas/equations and numbers in those formulas/equations to receive credit.)

In the following picture QS and PR are chords of the circle Find the length of QS Remember to show formulasequations and numbers in those formulasequations to r class=

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Answer: QS is 37 units long

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Explanation:

PN = 24 and NR = 14 are pieces of the chord PR. The two pieces multiply to some value. At the same time, the other two pieces QN = 21 and NS = 2x-4 also multiply to that same value. In short, the chord pieces multiply to the same number. This is known as the intersecting chord theorem.

PN*NR = QN*NS

24*14 = 21*(2x-4)

336 = 42x-84

336+84 = 42x-84+84 .... add 84 to both sides

420 = 42x

42x = 420

42x/42 = 420/42 ...... divide both sides by 42

x = 10

We know that x = 10 so we can use it to find the length of NS

NS = 2x-4

NS = 2*10-4

NS = 20-4

NS = 16

Therefore,

QS = QN + NS

QS = 21 + 16

QS = 37

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note: as a check,

PN*NR = QN*NS

24*14 = 21*16

336 = 336

we get a true equation, so we have the proper values

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