Final answer:
By applying the Chord-Chord Product Theorem, we determined that the length of chord QT in a circle is 18 cm.
Step-by-step explanation:
To find the value of x, which represents the length of chord QT, we can utilize the properties of chords in a circle. When two chords intersect inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. This is known as the Power of a Point Theorem or the Chord-Chord Product Theorem.
Applying this theorem to chords PTR and QTS, we set up the equation:
PT × RT = QT × ST
Substitute the given lengths:
16 cm × 9 cm = x cm × 8 cm
Multiply out the lengths on the left side of the equation:
144 cm² = 8x cm²
Divide both sides by 8 cm to solve for x:
x = 144 cm² / 8 cm = 18 cm
Thus, the length of chord QT is 18 cm.