Question

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

Answer 1

The correct answer is: (Option A) 100

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)

Answer 2

A
because
260 + df = 360
df = 360 - 260
df = 100