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lesantik [10]
1 year ago
15

Outline the process for inscribing a regular hexagon in a circle. Perform the construction in GeoGebra

Mathematics
1 answer:
mr_godi [17]1 year ago
4 0

The following are the general steps to draw a hexagon inscribed in a circle:

First draw a circle with center A through B:

Then the intersection points will be vertex C and vertex D of the hexagon. Doing this for each vertex (from left to right) we will get the following:

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Find the center of the circle that you can circumscribe about ABC A=(-1,-2) B=(-5,-2) C=(-1,-7)
Luda [366]

Answer:

O : (-3,-4.5)

Step-by-step explanation:

center of circle: O (x.y)

Radius (r) = OA = OB = OC

r² = (x - (-1))² + (y - (-2))² ---- OA²  

r² = (x - (-5))² + (y - (-2))² ---- OB²

r² = (x - (-1))² + (y - (-7))² ---- OC²

OA²=OB² : (x - (-1))² + (y - (-2))² =  (x - (-5))² + (y - (-2))²

(x+1)² - (x+5)² = 0       x²+2x+1-x²-10x-25 = 0

8x = -24

x = -3

OA² = OC²   (x - (-1))² + (y - (-2))² = (x - (-1))² + (y - (-7))²

y²+4y+4 = y² +14y +49

10y = -45

y = - 4.5

O : (-3,-4.5)

6 0
3 years ago
Find the value of <br> x<br> y, and <br> z in the parallelogram below.
EastWind [94]
Let A be the angle of 79 degrees
B be the angle of (5y-4) degrees
C be the angle of (x+5) degrees
D be the angle of (9z-7) degrees
According to the property of parallelogram
Opposite angles are equal
We get, angle A = angle C
Since angle A = 79 degrees
And angle C = (x+5) degrees
We get, x+5=79
=> x=79-5=74.

Angle B = Angle D
(5y-4)=(9z-7)
Since there’s two variables here, we can’t use the property of “opposite angles are equivalent”
We have to use another property which is adjacent angles are equal
Therefore, we can find angle D
Angle D + Angle A=180
=> 9z-7 =180-79
z=108/9
z=12
Since (5y-4)=(9z-7)
Substitute z=12 in
We get, 5y-4=101
y= 105/5
y= 21
Therefore, x=74, y=21 and z=12.
6 0
1 year ago
Which of the following will result in a rational answer? Which number is not a rational number?
defon

Answer:

what are the #

Step-by-step explanation:??

3 0
3 years ago
The circle has an area of 144 <br><br> What is the radius and diameter
vichka [17]

Answer:

for the radius, the cloest i could get was 6.77. therefore the diametre would be double meaning its would be 13.54

so sorry if this is incorrect!

8 0
2 years ago
Read 2 more answers
Prove that the triangle EDF is isosceles. Give reasons for your answer.
Gekata [30.6K]

Answer:

\triangle EDF is isosceles.

Step-by-step explanation:

Please have a look at the attached figure.

We are <u>given</u> the following things:

\angle EDF = y

\text{External }\angle DFG = 90 +\dfrac{y}{2}

Let us try to find out \angle E and \angle DFE. After that we will compare them.

<u>Finding </u>\angle DFE<u>:</u>

Side EG is a straight line so \angle GFE = 180

\angle GFE is sum of internal \angle DFE and external \angle DFG

\angle GFE = 180 = \angle DFE  + \angle DFG\\\Rightarrow 180 = \angle DFE + (90+\dfrac{y}{2})\\\Rightarrow \angle DFE = 180 - 90 - \dfrac{y}{2}\\\Rightarrow \angle DFE = 90 - \dfrac{y}{2} ....... (1)

<u>Finding </u>\angle E<u>:</u>

<u>Property of external angle:</u> External angle in a triangle is equal to the sum of two opposite internal angles of a triangle.

i.e. external \angle DFG = \angle E + \angle EDF

\Rightarrow 90+\dfrac{y}{2} = \angle E + y\\\Rightarrow \angle E = 90+\dfrac{y}{2}  -y\\\Rightarrow \angle E = 90-\dfrac{y}{2} ....... (2)

Comparing equations (1) and (2):

It can be clearly seen that:

\angle DFE = \angle E =90-\dfrac{y}{2}

The two angles of \triangle EDF are equal hence \triangle EDF is isosceles.

8 0
3 years ago
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