Given: Circle X with a Radius r and circle Y with radius s Prove: Circle x is similar to circle y

Mathematics

2 answers:

lana [24]2 years ago

8 0

Two figures are similar if one is the scaled version of the other.

This is always the case for circles, because their geometry is fixed, and you can't modify it in anyway, otherwise it wouldn't be a circle anymore.

To be more precise, you only need two steps to prove that every two circles are similar:

Translate one of the two circles so that they have the same center
Scale the inner circle (for example) unit it has the same radius of the outer one. You can obviously shrink the outer one as well

Now the two circles have the same center and the same radius, and thus they are the same. We just proved that any two circles can be reduced to be the same circle using only translations and scaling, which generate similar shapes.

Recapping, we have:

Start with circle X and radius r
Translate it so that it has the same center as circle Y. This new circle, say X', is similar to the first one, because you only translated it.
Scale the radius of circle X' until it becomes $s$ . This new circle, say X'', is similar to X' because you only scaled it

So, we passed from X to X' to X'', and they are all similar to each other, and in the end we have X''=Y, which ends the proof.

stealth61 [152]2 years ago

5 0

Answer:

Step-by-step explanation:

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slamgirl [31]

The formula for a diagonal of a rectangle is √w^2+h^2, with w and h being the width and height. Plug in your numbers to get √7^2+5.5^2. Simplify that into √49+30.25, then to √79.25. Use your calculator to get 8.9022. The diagonal is 8.9 feet.

5 0

2 years ago

The coordinates of the vertices for the figure HIJK are H(0, 5), I(3, 3), J(4, –1), and K(1, 1).

pogonyaev

Answer: The quadrilateral HIJK is a parallelogram.

Explanation:

It is given that the coordinates of the vertices for the figure HIJK are H(0, 5), I(3, 3), J(4, –1), and K(1, 1).

The parallelogram diagonal theorem states that the quadrilateral is a parallelogram if both diagonal bisects each other.

If HIJK is a quadrilateral, then HJ and IK are the diagonals of HIJK.

First we find the midpoint of HJ.

$\text{Midpoint of HJ}=(\frac{0+4}{2}, \frac{5-1}{2})$