Question

In the accompanying diagram of circle O, mAB = 64 and m AEB = 52

What is the measure of CD?

Answer 1

`\huge\boxed{\sf CD = 40}`

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:

`\displaystyle \angle AEB=(1)/(2) (arc \ AB + arc \ CD)`

Solution:

Put the givens in the formula.

`\displaystyle 52 = (1)/(2) (64 + CD)\\\\Multiply \ both \ sides \ by \ 2\\\\52 * 2 = 64 + CD\\\\104 = 64 + CD\\\\Subtract \ 64 \ from \ both \ sides\\\\104 - 64 = CD\\\\40 = CD\\\\CD = 40 \\\\\rule[225]{225}{2}`