Question

Return to the Dynamic Geometry Tool. Select D then A > Construct > Circle by Center + Point.
Similarly construct circles with radius DB and radius DC. How are the pre-image, center of
rotation, and image of a point related?


a) The image and pre-image are not on the same circle

b) the image and pre-image points are on the same circle

c) can not be determined from information given

Answer 1

All circles are similar but all circles are not congruent.

The true statement is that:  b) the image and pre-image points are on the same circle

From the complete question, we understand that:

• Point B and C are the centers of both circles, respectively
• Point D is a common point on both circles

The above statements means that:

Point D is equidistant from point B and point C

In other words

$\mathbf{DB = DC}$

This can further be rewritten as:

$\mathbf{radius = DB = DC}$

The above statement means that:

The radii of both circles are equal

When two circles have the same radius, then the circles are similar and congruent

Hence, the true statement is option (b):

See attachment for the illustration of circle constructions

Read more about circles at:

https://brainly.com/question/9297897