Question

and the feature below, two chords intersect inside the circle at point U. suppose that UM = 26, UJ = 13, and UK =39. Find UN.

Answer 1

The Intersecting Chords theorem states that the products of the line segments on each chord are equal. In other words,

$UM\cdot UN=UJ\cdot UK$

We already know that UM = 26, UJ = 13, and UK = 39. Putting these values in the above equation gives us

$26\cdot UN=13\cdot39$$26\cdot UN=507$

Dividing both sides by 26 gives

$\textcolor{#FF7968}{UN=19.5.}$

which is our answer!