Question

1. a find the exact circumference of the circle below.

b. find the measure of arc aec.
c=
c=
c=

Explanation:

Step1: Find the diameter of the circle

Since \(\angle ADC = 90^{\circ}\), by the Thales' theorem, \(AC\) is the diameter of the circle. Using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 3\) and \(b=4\). So \(AC=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5\) cm.

Step2: Calculate the circumference of the circle

The formula for the circumference of a circle is \(C=\pi d\), where \(d\) is the diameter. Substituting \(d = 5\) into the formula, we get \(C = 5\pi\) cm.

Step3: Find the measure of arc \(AEC\)

The measure of a semic - circle is \(180^{\circ}\). Arc \(AEC\) is a semic - circle.

Answer:

A. \(C = 5\pi\) cm
B. The measure of arc \(AEC\) is \(180^{\circ}\)