Question

(b) in the figure below, two chords intersect inside the circle at point u. suppose that uk = 27, un = 13.5, and uj = 18. find um. um =

Explanation:

Step1: Recall the intersecting chords theorem

When two chords intersect inside a circle, the products of the lengths of their segments are equal. So, \( UJ \times UM = UK \times UN \).

Step2: Substitute the given values

We know \( UJ = 18 \), \( UK = 27 \), \( UN = 13.5 \). Let \( UM = x \). Then the equation becomes \( 18 \times x = 27 \times 13.5 \).

Step3: Solve for \( x \)

First, calculate the right - hand side: \( 27\times13.5 = 364.5 \). Then, to find \( x \), we divide both sides of the equation \( 18x = 364.5 \) by 18. So, \( x=\frac{364.5}{18}=20.25 \).

Answer:

\( 20.25 \)