Question

The circum radius of the triangle with vertices (1, 0), (7,0) and (4, 5) is​

Answer 1

What is the circumradius of a triangle when its vertices are (0,0), (3,0) and (1,4/3)?

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The vertices of the triangle are A(0,0),B(3,0) and C(1,43).

⇒ The lengths of the sides of the triangle are

BC=a=√4+169−−−−−√=52√3,

AC=b=1+169−−−−−√=53, and

AB=c=3.

The length of the altitude from vertex C to side AB is 43.

⇒ The area of △ABC is 12(base×height)=12(3×43)=2.

The formula for the circumradius of a triangle is R=abc4A, where a,b and c are t

What is the circumcenter of the triangle with vertices (0, 0) (3, 0) and (0, 4)?

What is the circumcenter of a triangle with vertices (0,0), (2,4), and (3,6)?

What is the circumcenter of a triangle whose vertices are (0,0), (-8,0) and (0,6)?

What is the circumcentre of a triangle whose vertices are (-3 , 3) (0, -1) (3,0)?

If the coordinates of the vertices of a triangle is (3,0), (-1,-6), (4,-1) respectively, what is its circumcenter and circumradius?

The circumradius is the product of the sides divided by four times the area. It’s usually more convenient squared:

R2=a2b2c216Δ2

We have squared sides

32=9

12+(4/3)2=25/9=52/32

(3−1)2+(4/3)2=52/9=22(13)/32

We can get the area any number of ways; base is 3 along x axis, height 4/3, so area

Δ=12(3)(4/3)=2

R2=(32)(52/32)(22(13)/32)16(22)

R2=52(13)4232

R=51213−−√

Answer 2

Answer:

The circum radius of the triangle with vertices (1, 0), (7,0) and (4, 5) is​ 3.75

Step-by-step explanation:

From the above question,

They have given :

       The circumradius of a triangle is the radius of the circle that circumscribes the triangle, that means it passes thru all three vertices. To discover the circumradius, we need to calculate the size of the facet contrary the attitude we are searching for, the use of the Pythagorean Theorem.

Calculate the size of the aspect contrary the attitude the use of the Pythagorean Theorem:

                             $a^2 + b^2 = c^2.$

In this case, the side length is 6, so $a^2 + b^2 = 6^2 + 5^2$ = 61.

Take the rectangular root of each aspects to get the circumradius: √61 = 3.75.

In this case, the side opposite the angle formed by the vertices (1, 0), (7, 0) and (4, 5) is 6, so the circumradius is √$(6^2 + 5^2)$ = √61 = 3.75.

Calculate the length of the side opposite the angle using the Pythagorean Theorem:

                             $a^2 + b^2 = c^2.$

In this case, the side length is 6, so $a^2 + b^2 = 6^2 + 5^2$ = 61.

In this case, the facet contrary the attitude fashioned by way of the vertices (1, 0), (7, 0) and (4, 5) is 6, so the circumradius is √61 = 3.75.

In this case, the side opposite the angle formed by the vertices (1, 0), (7, 0) and (4, 5) is 6, so the circumradius is √$(6^2 + 5^2)$ = √61 = 3.75.

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