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DaniilM [7]
2 years ago
15

Use the circle to solve for the missing measures. Assume lines that appear tangent are tangent. Do NOT round any answers.

Mathematics
1 answer:
wlad13 [49]2 years ago
4 0

The given circle having two external tangents, according to circle

theorem, have the following values;

  • r = 3
  • m∠1  = 82°
  • m∠2 = 49°
  • x = 82°

<h3>How can the radial  length and angles be found?</h3>

r² + 1.6² = (0.4 + r)²

(0.4 + r)² - (r² + 1.6²) = 0

0.8·r - 2.4 = 0

0.8·r = 2.4

r = 2.4 ÷ 0.8 = 3

  • <u>r = 3</u>

y = 49°

From the two tangent angle theorem, we have;

m∠1 = ((82 + 98 + 82) - (360 - ((82 + 98 + 82)))) ÷ 2 = 82

  • <u>m∠1  = 82°</u>

According to circle theorems, angle at the center is twice angle

subtended at the circumference.

m∠2 = (360 - (82 + 98 + 82)) ÷ 2 = 49°

  • <u>m∠2 = 49°</u>

The length of the chord subtended by the arc <em>x</em> is equal to the length of

the chord subtended by 89°, which gives;

  • <u>x = 82°</u>

Learn more about circle theorems applications here:

brainly.com/question/16879446

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PLEASE HELP I CANT FAIL
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Answer:

A) Miguel: d=25t+10

gabby: d=30t

B) gabby will catch up with Miguel in 2 hours at a distance of 60 miles

Step-by-step explanation:

<u><em>Lets start of with the equation:</em></u>

There is 2 possible equations we can use for this:

  1. A) Miguel: d=25t+10  gabby: d=30t     OR
  1. D) Miguel: d=10t+25  gabby: d= 30t

The resonable response for this would be A because Miguel starts off with 10 miles so you would add 10 to your equation so response D is incorrect because you are not multiplying 10t, but rather 25t.

<u><em>Now let's do the actual answer</em></u>

There is 2 possible answer for this:

  1. B) gabby will catch up with Miguel in 2 hours at a distance of 60 miles
  2. C) gabby will catch up with Miguel in 1.25 at a distance of 37.5 miles

The response that would make the most sense would be B. Let me explain

We are going to be using response C for now. You would have to multiply Miguel: 25(1.25) + 10

31.25 + 10

=41.25

Gabby: 30(1.25)

= 37.50

Miguel is still ahead of Gabby so Answer C is incorrect

We are going to be using response B now. You would have to multiply

Miguel: 25(2) + 10

50 + 10

=60

Gabby: 30(2)

=60

Now they are both the same mile so this would mean Answer B is correct

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