Question

Watch your lateral PQRS is inscribed in circle O. Opposite angles, P and R measure (x+16)* and (6x-4)* respectively. Determine the measure of the smaller angle.
Answer
Circle with the radius of 6 inches is dilated by a scale factor of four what is the radius of the transformed circle?
Answer
If circle O has a circumference of 37 m in circle P has a circumference of 111 m then what is the scale factor from O to P
Answer
If circle a has a radius of 6 mm with a circumference of approximately 38 m in circle B has a radius of 60 mm and what is circle B is approximate circumference
Answer
If circle ax is constructed so that it has a circumference of 120 cm and is dilated to create circle X’ with a circumference of 90 cm and what is a scale factor
Answer
If the radius of Circle B is 13 feet and the radius of circle C is 78 feet then what is the scale factor from circle B to circle C
Answered by GPT 3.5
Since PQRS is inscribed in circle O, opposite angles are supplementary. Therefore, we can set up the equation:

(x+16)* + (6x-4)* = 180*

Expanding the equation:

x + 16 + 6x - 4 = 180
7x + 12 = 180
7x = 168
x = 24

Now we can plug in the value of x into the angle measurements:

Angle P = (24+16)* = 40*
Angle R = (6*24 - 4)* = 140*

Therefore, the smaller angle is angle P, which measures 40 degrees.
Answered by GPT 3.5
When a figure is dilated by a scale factor, all its dimensions increase by that scale factor. In this case, the scale factor is 4.

The radius of the original circle is 6 inches. When dilated by a scale factor of 4, the new radius of the transformed circle will be:

6 inches * 4 = 24 inches

Therefore, the radius of the transformed circle is 24 inches.
Answered by GPT 3.5
The circumference of a circle is given by the formula 2πr, where r is the radius of the circle.

For circle O:
Circumference of O = 2πr = 37m

For circle P:
Circumference of P = 2πR = 111m

We want to find the scale factor from circle O to circle P. Since circumference is directly proportional to the radius, we can set up the following proportion:

(2πR)/(2πr) = 111m/37m

R/r = 111m/37m
R/r = 3

Therefore, the scale factor from circle O to circle P is 3.
Answered by GPT 3.5
To find the circumference of circle B, we can use the formula for the circumference of a circle, C = 2πr, where r is the radius of the circle.

For circle A:
Radius, r = 6 mm
Circumference, C = 38 m = 38000 mm (because 1 m = 1000 mm)

We can calculate the circumference of circle A using the formula:
C = 2π(6) = 12π ≈ 37.699 mm

Now, we can set up a proportion to find the circumference of circle B:
C(circle B) / r(circle B) = C(circle A) / r(circle A)

C(circle B) / 60 = 37699 / 6
C(circle B) / 60 = 6283.16
C(circle B) = 60 * 6283.16
C(circle B) ≈ 376989.6 mm

So, the approximate circumference of circle B is approximately 376989.6 mm.
Answered by GPT 3.5
When a shape is dilated, all corresponding linear measurements are increased or decreased by the same scale factor.

Let the scale factor be represented by "k".

For circle AX with circumference 120 cm:
Circumference of AX = 2πr = 120 cm

For circle X' with circumference 90 cm:
Circumference of X' = 2π(kr) = 90 cm

We can set up the proportion involving the circumferences of the two circles:
2π(kr) / 2πr = 90 / 120
k = 90/120
k = 3/4

Therefore, the scale factor from circle AX to circle X' is 3/4.
Answered by GPT 3.5
The scale factor from one circle to another is typically determined by comparing the radii of the circles. The scale factor is equal to the ratio of the radius of one circle to the radius of the other circle.

In this case:
Radius of circle B = 13 feet
Radius of circle C = 78 feet

To find the scale factor from circle B to circle C, we use the formula:

Scale factor = Radius of circle C / Radius of circle B
Scale factor = 78 feet / 13 feet
Scale factor = 6

Therefore, the scale factor from circle B to circle C is 6. This means that the radius of circle C is 6 times larger than the radius of circle B.