In a circle of radius 6 cm and center O.  PQ and PR are two equal chords, each of length 8 cm.  What is the length (in cm) of chord QR?

\(\frac{16\sqrt {5}}{3}\)

OX = \(\sqrt {36 - 16}\) = 2\(\sqrt {5}\)

Let draw a perpendicular bisector from center O to QR

\(\frac{1}{2}\) × O × x × QP = \(\frac{1}{2}\) × PO × QN

2\(\sqrt {5}\) × 8 = 6 × QP

QN = \(\frac{8\sqrt {5}}{3}\)

QR = 2QN = \(\frac{16\sqrt {5}}{3}\)