1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
olga2289 [7]
2 years ago
13

The circumcenter is the center of the. circle

Mathematics
2 answers:
lilavasa [31]2 years ago
6 0

Answer: Another name of circumcenter is, " Circumscribed circle ". The circumcenter is the center point of the circumcircle drawn around a polygon. The circumcircle of a polygon is the circle that passes through all of the polygon's vertices & the center of that circle is called the circumcenter. All polygons that have circumcircles are known as cyclic polygons. However, all polygons does not have a circumcircle. Only <u>regular polygons, triangles, rectangles, and right-kites</u> can have the circumcircle and thus the circumcenter as well.

You may find that the circumcenter of a triangle as the most common thing asked in exams and it is generally what schools begin with. So, some brief information about the circumcenter of a triangle is given below. You may safely ignore them if you haven't learned them yet.

<h3>What is the Circumcenter of a Triangle?</h3>

The circumcenter of triangle can be found out as the intersection of the perpendicular bisectors (the lines that are at right angles to the midpoint of each side) of all sides of the triangle. This means that the perpendicular bisectors of the triangle are concurrent (meeting at one point). All triangles are cyclic and hence, can circumscribe a circle, therefore, every triangle has a circumcenter.

<h3>Properties of Circumcenter of Triangle</h3>

Property 1: All the vertices of the triangle are equidistant from the circumcenter.

Property 2: All the new triangles formed by joining O to the vertices are Isosceles triangles.

Property 3: Circumcenter lies at the midpoint of the hypotenuse side of a right-angled triangle

Property 4: In an acute-angled triangle, circumcenter lies inside the triangle

Property 5: In an obtuse-angled triangle, it lies outside of the triangle

<u>Note</u>- Location for the circumcenter is different for different types of triangles.

<h3>How to construct Circumcenter of a Triangle?</h3>

The circumcenter of any triangle can be constructed by drawing the perpendicular bisector of any of the two sides of that triangle. The steps to construct the circumcenter are:

  • Step 1: Draw the perpendicular bisector of any two sides of the given triangle.
  • Step 2: Using a ruler, extend the perpendicular bisectors until they intersect each other.
  • Step 3: Mark the intersecting point as P which will be the circumcenter of the triangle. It should be <u>noted </u>that, even the bisector of the third side will also intersect at P.
<h3>
Circumcenter Formula</h3>

P(X, Y) = [(x1 sin 2A + x2 sin 2B + x3 sin 2C)/ (sin 2A + sin 2B + sin 2C), (y1 sin 2A + y2 sin 2B + y3 sin 2C)/ (sin 2A + sin 2B + sin 2C)]

 ∩_∩
(„• ֊ •„)♡
┏━∪∪━━━━┓
  hope it helped
┗━━━━━━━┛

erma4kov [3.2K]2 years ago
4 0

The circumcenter is the center of the circle which goes through the triangle's vertices, so the circumcenter of the triangle and the center of that circumscribed circle MUST be the same point.

The same goes for the incenter and the center of the inscribed circle, though these will not, in general, be the same point as the circumcenter.

You might be interested in
Which ratio correctly compares 60 mm to 45 cm?
Agata [3.3K]
60 mm converts to 6 centimeters.
the ratio of 6 to 45 can be simplified to 
2 : 15
8 0
3 years ago
Use and list a line of your choice that's neither horizontal nor vertical to reflect the object and show where it ends up.
EastWind [94]
Ughhh I’m not totally sure I’m sorry I tried looking it up for you
4 0
3 years ago
An angle that has a supplement also has a complement. Always, sometimes, or never?
Assoli18 [71]
So the problem ask to what could be the right choice among the three that could support the said statement in you problem that tells that an angle that has a supplement also has a complement and the best answer would be that it is ALWAYS be TRUE. I hope you are satisfied with my answer 
8 0
3 years ago
Does anyone know the answer?
azamat

Answer:

1=163 degrees

2=×=10 degrees

3=×=3

Step-by-step explanation:

54x+1+9x-10=180 we are using this expression because alternate angles add up to 180 degrees

54x+9x+1-10=180

63x-9=180

63×=180+9

63×=189

63×÷63×=189÷63×

X=3

Angle in bold print is (54x+1)

54×3=162

162+1=163 degrees

No.2 Find x

7x+35+x+65 =180

7x+x+35×65=180

8x+100=180

8x=180-100

8x=80

8x÷8x=80÷8

X=10 degrees

No.3 Find x

54x+1+9x-10=180

54x+9x+1-10=180

63x-9=180

63x=180+9

63x=189

63x÷63x=189÷63

X=3

I hope I was of help

6 0
3 years ago
Look at the picture and answer it please
AysviL [449]
The first choice is substitution because G s being substituted by C
5 0
3 years ago
Other questions:
  • 30% of what number is 9
    10·1 answer
  • What is the answer of this
    10·2 answers
  • Ok serous question this has nothing to do with my other questions would you guys care if I committed ya know
    10·2 answers
  • Which of the following numbers is a composite number that is divisible by 5?
    11·2 answers
  • F(x)=3x+5/x, what is f(a-2)
    7·1 answer
  • Helpp i will give brainiest
    7·1 answer
  • Ten more than four times a number is equal to the difference between 73 and three times the number. Find the number.
    12·1 answer
  • Math To Do, Ready
    9·1 answer
  • PLEASE ANSWER THIS QUESTION
    9·2 answers
  • A man has a collection of 19 coins worth $2.55. There are twice as many nickels as dimes. If the rest are quarters, how many qua
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!