Question

In the figure below, \overline{AD} AD start overline, A, D, end overline and \overline{BE} BE start overline, B, E, end overline are diameters of circle PPP. What is the arc measure of \stackrel{\LARGE{\frown}}{CD} CD ⌢ C, D, start superscript, \frown, end superscript in degrees? ^\circ ∘ degrees

Answer 1

Answer:

The measure of the arc CD = 64°

Step-by-step explanation:

The rest of the question is the attached figure.

It is required to find the measure of the arc CD in degrees.

as shown at the graph

BE and AD are are diameters of circle P

And ∠APE is a right angle ⇒ ∠APE = 90°

∠APE and ∠BPE are supplementary angles

So, ∠APE + ∠BPE = 180°

∠BPE + 90 = 180°

∴ ∠BPE = 180 -90 = 90° ⇒(1)

But it is given: ∠BPE = (33k-9)° ⇒(2)

From (1) and (2)

∴ 33k - 9 = 90

∴ 33k = 90 + 9 = 99

∴ k = 99/33 = 3

The measure of the arc CD = ∠CPD = 20k + 4

By substitution with k

∴ The measure of the arc CD = 20*3 + 4 = 60 + 4 = 64°

Answer 2

Applying the central angle theorem, the measure of arc CD is: 64°.

What is the Central Angle Theorem?

The central angle theorem states that, the measure of the central angle is always the same as the measure of the intercepted arc in a circle.

Since AD and BE are diamaters dividing the circle into semicircles, therefore:

m∠DPE = 90°

33k - 9 = 90

33k = 90 + 9

33k = 99

k = 3

m∠CPD = 20k + 4

Plug in the value of k

m∠CPD = 20(3) + 4 = 64°

Arc measure of CD = m∠CPD [central angle theorem]

Arc measure of CD = 64°.

Thus, applying the central angle theorem, the measure of arc CD is: 64°.

Learn more about central angle theorem on:

https://brainly.com/question/5436956