Question

In circle O, MN = PQ,
MN = 7x + 13, and
PQ = 10x - 8. Find PS.

Answer 1

• 31 units

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Use the fact that the two chords are congruent and solve for x:

• MN = PQ

• 7x + 13 = 10x - 8
• 10x - 7x = 13 + 8
• 3x = 21
• x = 7

Find the length of PQ:

• PS = 10*7 - 8 = 62

PS is half the PQ since OS is the perpendicular bisector of PQ:

• PS = PQ/2
• PS = 62/2
• PS = 31