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xeze [42]
3 years ago
13

All sides of quadrilateral ABCD ABCD A, B, C, D are tangent to circle PPP. What is the perimeter of the quadrilateral below?

Mathematics
1 answer:
noname [10]3 years ago
4 0

Answer:

The answer is below

Step-by-step explanation:

A tangent is a line which touches a circle at one point. The angle between a tangent and a circle is 90°.

The two tangent theorem states that tangent that meet at the same point are equal in length.

Therefore:

CD = c + d

but c = 5.1, hence:

CD = 5.1 + d

12.1 = 5.1 + d

d = 7

AD = a + d; but AD = 12.2, d = 7

12.2 = a + 7

a = 5.2

AB = a + b; but b = 3.3

AB = 5.2 + 3.3 = 8.5

BC = b + c = 3.3 + 5.1 = 8.4

Perimeter of ABCD = AB + BC + CD + AD = 8.5 + 8.4 + 12.1 + 12.2 = 41.2

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If JKLM is a rhombus, MK = 30, NL = 13, and mZMKL = 41°, find each measure.
oksian1 [2.3K]

Answer:

NK = 15

JL = 26

KL = 19.85

\angle JKM =49

\angle JML =41

\angle MLK = 90

\angle MNL =90

\angle KJL =41

Step-by-step explanation:

Given

MK = 30

NL = 13

\angle MKL = 41

Solving (a): NK

MK is a diagonal and NK is half of the diagonal. So:

NK = \frac{1}{2} * MK

NK = \frac{1}{2} * 30

NK = 15

Solving (b): JL

JL is a diagonal, and it is twice of NL.

JL = 2 * NL

JL = 2 * 13

JL = 26

Solving (c): KL

To solve for KL, we consider triangle KNL where:

\angle KNL = 90

and

KL^2 = NL^2 + NK^2

KL^2 = 13^2 + 15^2

KL^2 = 394

KL = \sqrt{394

KL = 19.85

Solving (d - h):

To do this, we consider triangle JKN

\angle KNL = \angle LNM = \angle MNJ = \angle JNK = 90 -- diagonals bisect one another at right angle

Alternate interior angles are equal. So:

\angle MKL = \angle KMJ = \angle KJL = \angle JLM = 41

Similarly:

\angle MKJ = \angle KML = \angle MJL = \angle JLK = 90 - 41

\angle MKJ = \angle KML = \angle MJL = \angle JLK = 49

So:

\angle JKM =49

\angle JML =41

\angle MLK = \angle MLJ + \angle JLK

\angle MLK = 49 + 41

\angle MLK = 90

\angle MNL =90

\angle KJL =41

5 0
3 years ago
150 people in 5 classes
Firdavs [7]
150 = 5 classes
1 class = 30
4 0
3 years ago
Algebra help please !
umka2103 [35]

Answer:

g(f(0)) = 2

Step-by-step explanation:

To find g(f(0)), you must first find f(0).

f(x) = 3x + 1

f(0) = 3(0) + 1 = 0 + 1 = 1

Now you input 1 into function g(x).

g(x) = (4x + 2)/3

g(1) = [4(1) + 2]/3

g(1) = [4 + 2]/3

g(1) = 6/3

g(1) = 2

g(f(0)) = 2

6 0
3 years ago
Read 2 more answers
Carmen Martinez
klemol [59]
  • (4,4)
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\boxed{\sf Slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}

\\ \sf\longmapsto m=\dfrac{7-4}{10-4}

\\ \sf\longmapsto m=\dfrac{3}{6}

\\ \sf\longmapsto m=\dfrac{1}{2}

\\ \sf\longmapsto m\approx0.5

6 0
3 years ago
Read 2 more answers
How much inches is 5 feet ​
Elza [17]

Answer:

60 inches

Step-by-step explanation:

7 0
3 years ago
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