Question

1. (07.01 mc)

for circle h, \\(jn = 5\\), \\(nk = 4\\), \\(ln = 2\\), and \\(nm = x\\). solve for \\(x\\). (1 point)

10
2.5
1.6
7

Explanation:

Identify the geometric theorem

The problem shows two chords, \(JK\) and \(LM\), intersecting inside circle \(H\) at point \(N\). To find the unknown length \(x\), we can apply the Intersecting Chords Theorem. This theorem states that when two chords intersect inside a circle, the products of their segments are equal.

Set up the equation

According to the Intersecting Chords Theorem, the segments of chord \(JK\) and chord \(LM\) satisfy the following relation:

$$JN \cdot NK = LN \cdot NM$$

Substitute the given values

We are given the following segment lengths:

• \(JN = 5\)
• \(NK = 4\)
• \(LN = 2\)
• \(NM = x\)

Substituting these values into our relation gives:

$$5 \cdot 4 = 2 \cdot x$$

Solve for x

Simplify the equation to find the value of \(x\):

$$20 = 2x$$

$$x = \frac{20}{2}$$

$$x = 10$$

Answer:

• (A) 10 (Correct answer)
• (B) 2.5
• (C) 1.6
• (D) 7