9. Find ME.

Let's analyze the geometry problem step by step. 1. Understanding the Problem: We have a circle with two intersecting chords, MN and FP. We are given the lengths NE = 3, EP = 6, and FE = 4. We need to find the length of ME. 2. Applying the Intersecting Chords Theorem: The Intersecting Chords Theorem states that when two chords intersect inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. In this case, we have: ME * NE = FE * EP 3. Setting up the Equation: Let ME = x. Then we have: x * 3 = 4 * 6 4. Solving for x: 3x = 24 x = 24 / 3 x = 8 Therefore, the length of ME is 8. Answer: 8