Question

56:22

In each circle below, a 50° angle with a vertex at the center of the circle is drawn. How are minor arc lengths CD and EF

related?

A <

50

BF

50°

2 cm

cm

They are the same because the central angle measure is the same.

The arc lengths are proportional: CD = 2 EF

Answer 1

C. The arc lengths are proportional: Arc C D = 4 arc E F.

Explanation:

The question is incomplete. Here is the complete question.

In each circle below, a 50° angle with a vertex at the center of the circle is drawn. How are minor arc lengths CD and EF related?

Circle A and B are shown. Line segments D A and C A are radii with lengths of 8 centimeters. Angle D A C is 50 degrees. Line segments F B and E B are radii with lengths of 2 centimeters. Angle F B E is 50 degrees.

They are the same because the central angle measure is the same.

The arc lengths are proportional: Arc C D = 2 arc E F.

The arc lengths are proportional: Arc C D = 4 arc E F.

The arc lengths are proportional: Arc C D = 6 arc E F.

Using the formula for calculating the length of an arc to find the length of both arcs.

`L = (\theta)/(360) * 2\pi r`

For the minor arc CD:

`\theta = 50^0\\`

r = 8cm

L = 50/360 * 2π(8)

L = 5/36 * 16π

L = 80π/36

Length of CD = 20π/9 cm²

For the minor arc EF:

`\theta = 50^0\\`

r = 2cm

L = 50/360 * 2π(2)

L = 5/36 * 4π

L = 20π/36

Length of arc EF = 5π/9 cm²

Find the relationship between both lengths:

From CD = 20π/9 cm²

CD = 4 * (5π/9 cm²)

since length of arc EF = 5π/9 cm²

Then arc CD = 4* arc EF

This shows that the length of arc CD is four times that of arc EF