Which transformation shows that the two given circles are similar? circle a -- center(2, 0), radius 8 circle a' -- center(-1, 5), radius 3

Step-by-step explanation:

One circle A with the center (2, 0) is transformed to a new point A' (-1, 5) means a circle is shifted to A' with new coordinates.

Therefore transformation done will be A [(2-x), (0-y)]

Here 2 - x = -1

-x = -2 - 1 = -3

x = 3

and 0-y = 5

y = -5

Therefore the transformation done is [(x - 3), (y +5)].

Now we see that the radius of the new circle is changed. Therefore new circle is enlarged with a scale factor of 3/8 = ( new radius/old radius)

So we conclude that a circle A is transformed to A' with [(x -3), (y + 5)]

and then enlarged by a scale factor of 3/8.

oof

step-by-step explanation:

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.