Question

find the value of ( x ). note that ( be = 12 ), ( ce = 15 ), ( de = x ), and ( ae = 16 ).

Explanation:

Step1: Apply intersecting chords theorem

For two intersecting chords in a circle, the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord: $AE \times BE = DE \times CE$

Step2: Substitute given values

Substitute $AE=16$, $BE=12$, $DE=x$, $CE=15$:
$16 \times 12 = x \times 15$

Step3: Calculate left-hand side

Compute $16 \times 12$:
$192 = 15x$

Step4: Solve for x

Isolate $x$ by dividing both sides by 15:
$x = \frac{192}{15}$

Step5: Simplify the fraction

Reduce the fraction to lowest terms:
$x = \frac{64}{5} = 12.8$

Answer:

$x = 12.8$ or $\frac{64}{5}$