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In the diagram below, and are tangent to O. What is the measure of arc DF ?

A. 100 B. 90 C. 80 D. 170

In the diagram below, and are tangent to O. What is the measure of arc DF ? A. 100 B-example-1

2 Answers

6 votes
A
because
260 + df = 360
df = 360 - 260
df = 100
User Uzo
by
8.2k points
4 votes

The correct answer is: (Option A) 100

Step-by-step explanation:

There are two methods to solve this problem.

IMPORTANT NOTE: Do not confuse "arc length" with "measure of arc." Measure of arc is actually the central angle's degree size!

Method-1:

Please see the attached image with the answer.

Since D and F are tangent to a circle. It means the lines DE and FE are at 90° with the radius of the circle DO and FO respectively. And sum of inner angles should be equal to 360°.

Now let us find the value of x (in the picture), which is the measure of arc DF:

80° + 90° + x + 90° = 360°

x = 100° (Option A)

Method-2:

Since the whole circle's measure is 360°. Therefore,

The blue arc + DF (green arc) = 360°

Blue arc = 260°

Therefore,

260° + DF (green arc) = 360°

DF (green arc) = 100° (Option A)

In the diagram below, and are tangent to O. What is the measure of arc DF ? A. 100 B-example-1
User Tumas
by
8.3k points

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