Question

the chords intersect at point u. what is the value of y? 12 cm 8 cm y cm 4 cm

Explanation:

Step1: Apply the intersecting chords theorem

When two chords intersect each other inside a circle, the products of the lengths of their segments are equal. So, \(QU\times US = RU\times UT\).

Step2: Substitute the given values

We know \(QU = 8\), \(US = y\), \(RU = 12\), and \(UT = 4\). Substituting these into the equation \(8\times y=12\times4\).

Step3: Solve for \(y\)

First, calculate \(12\times4 = 48\). Then the equation becomes \(8y = 48\). Divide both sides by \(8\), so \(y=\frac{48}{8}\).

Answer:

\(6\)