Question

the chords intersect at point u. what is the value of y? 2 4 6 8

Explanation:

Step1: Use the Chord - Chord Product Theorem

If two chords \(QR\) and \(ST\) intersect at a point \(U\) inside a circle, then \(QU\times US=RU\times UT\).
Here, \(QU = 8\space\text{cm}\), \(US=y\space\text{cm}\), \(RU = 12\space\text{cm}\), and \(UT = 4\space\text{cm}\).
Substitute the values into the formula: \(8\times y=12\times4\).

Step2: Solve the equation for \(y\)

The equation \(8y = 48\) (since \(12\times4 = 48\)).
Divide both sides of the equation by \(8\): \(y=\frac{48}{8}\).

Answer:

\(y = 6\)