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?
Answer & explanation
Correct answer: option 2
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 = \(\frac{16\sqrt {5}}{3}\)