Question

the chords intersect at point u.
what is the value of y?
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in the circle, chord qt and chord rs intersect at point u, where qu = 8 cm, ut = 4 cm, ru = 12 cm, us = y cm

Explanation:

Step1: Apply intersecting chords theorem

When two chords intersect in a circle, the products of the lengths of their segments are equal: $QU \times SU = RU \times TU$

Step2: Substitute known values

Substitute $QU=8$, $SU=y$, $RU=12$, $TU=4$:
$8 \times y = 12 \times 4$

Step3: Simplify and solve for y

Calculate right-hand side, then isolate y:
$8y = 48$
$y = \frac{48}{8}$

Answer:

6