Answer:
[tex]\huge\boxed{\sf CD = 40}[/tex]
Step-by-step explanation:
Given,
∠AEB = 52
arc AB = 64
Statement:
According to angles of intersecting chord theorem, when two chords intersect inside a triangle, the measure of angle formed by the chord equals one half of the sum of the two arcs subtended.
Mathematical form:
[tex]\displaystyle \angle AEB=\frac{1}{2} (arc \ AB + arc \ CD)[/tex]
Solution:
Put the givens in the formula.
[tex]\displaystyle 52 = \frac{1}{2} (64 + CD)\\\\Multiply \ both \ sides \ by \ 2\\\\52 \times 2 = 64 + CD\\\\104 = 64 + CD\\\\Subtract \ 64 \ from \ both \ sides\\\\104 - 64 = CD\\\\40 = CD\\\\CD = 40 \\\\\rule[225]{225}{2}[/tex]
