The polygon circumscribes a circle. What is the perimeter of the polygon?
The perimeter of the polygon is?

HELP PLZ

Polygons circumscribing a circle have tangents of equal lengths that come

from the same vertex that simplifies the calculation of the dimensions.

Reasons:

The polygon forms tangents to the circle, having the same external point

The lengths of the tangents drawn from the same external point are equal.

Therefore;

The length of the tangent on the other side of the tangent of given length and having the same external point are the same

Therefore, we have;

Two tangents of length 19 cm

Two tangents of length 9 cm

Two tangents of length 4 cm

and two tangents of length 6 cm

The above tangents reach round the perimeter of the polygon.

Therefore

The perimeter of the polygon = 19 + 19 + 6 + 6 + 4 + 4 + 9 + 9 = 76

The perimeter of the polygon = 76 cm

Learn more about tangents drawn from the same external point here:

link

Perimeter of the polygon is 76 cm

Step-by-step explanation:

There is a fact in the circle, the two tangents drawn from a point out side the circle are equal in length

Let us use this fact to solve the problem

∵ AB and AH are tangents to the circle

∵ A is out side the circle

∴ AB = AH

∵ AB = 9 cm

∴ AH = 9 cm

∵ CB and CD are tangents to the circle

∵ C is out side the circle

∴ CB = CD

∵ CB = 19 cm

∴ CD = 19 cm

∵ ED and EF are tangents to the circle

∵ E is out side the circle

∴ ED = EF

∵ EF = 6 cm

∴ ED = 6 cm

∵ GF and GH are tangents to the circle

∵ G is out side the circle

∴ GF = GH

∵ GF = 4 cm

∴ GH = 4 cm

The perimeter of the polygon is the sum of the lengths of its sides

∵ The sides of polygon ACEG are AC, CE, EG, and GA

∵ AC = 9 + 19 = 28 cm

∵ CE = 19 + 6 = 25 cm

∵ EG = 4 + 6 = 10 cm

∵ GA = 4 + 9 = 13 cm

∴ Perimeter of the polygon = 28 + 25 + 10 + 13

∴ Perimeter of the polygon = 76 cm

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

sorry i need the points

step-by-step explanation:

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