Mathematics, 11.01.2021 06:50 rakanmadi87

If T is the circumcenter of triangle MNP, find each measure.

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Applying the properties of circumcenter of a triangle and the Pythagorean Theorem, the measure of each given segments are calculated as:

8. TN = 22

9. RT = 12.8

Recall:

The point where the three perpendicular bisectors of a triangle meet is known as the circumcenter of the triangle.The perpendicular bisectors form right angles with each side it bisects. This means that there are two opposite right angles formed at point Q, S, and R.The circumcenter is also the point that is equidistant to all three vertices of the triangle. This means that, in the diagram given, MT, TN, and TP are equal.Pythagorean theorem can be used to solve for the missing side of a right triangle. It states that, if c is the hypotenuse (longest side that is directly opposite to the right triangle), and a and b are the two other smaller sides, therefore: c^2 = a^2 + b^2

8. Find TN

Given,

MT = 6x - 56TP = 3x - 17

Thus,

6x - 56 = 3x - 17 (MT = TN = TP, because they are equidistant from the circumcenter, T.)

Combine like terms

6x - 3x = 56 - 17

3x = 39

Divide both sides by 3

x = 13

TN = TP = 3x - 17

TN = 3x - 17

Plug in the value of x

TN = 3(13) - 17

TN = 22

9. Find RT

Given,

RN = 14TN = 4x - 17TP = x + 10

Thus,

4x - 17 = x + 10 (TN = TP)

Combine like terms

4x - x = 17 + 10

3x = 27

Divide both sides by 3

x = 9

TN = 4x - 17

Plug in the value of x

TN = 4(9) - 17

TN = 19

To find RT, apply the Pythagorean Theorem

$RT = \sqrt{TN^2 - RN^2}$

Substitute

$RT = \sqrt{19^2 - 14^2}\\\\\mathbf{RT = 12.8}$

In summary, applying the properties of circumcenter of a triangle and the Pythagorean Theorem, the measure of each given segments are calculated as:

8. TN = 22

9. RT = 12.8

Learn more about circumcenter of a triangle here:

link

If T is the circumcenter of triangle MNP, find each measure.

Answer from: mcmccann4317

8). TN = 22 units ; 9). √165

Step-by-step explanation:

The circumcenter of a triangle is the point in the plane equidistant from the three vertices of the triangle.

8). 6x - 56 = 3x - 17

3x = 39

x = 13

TN = 22 units

9). 4x - 17 = x + 10

3x = 27

x = 9

TN = 19

RT = $\sqrt{TN^2 - RN^2}$

RT = $\sqrt{361-196}$ = √165 ≈ 12.8 units

Answer from: Quest

step-by-step explanation:

107 units

Answer from: Quest

answer: haha (: i’ll go see what it is

step-by-step explanation:

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