College Geometry

Question

Five diagrams are given below. 

Based on the above diagrams, which of the following statements are true? 

Create an answer using the numbers associated with the true statements. For example, if only 1, 2, and 5 are true, then the answer is 125; if only 3 and 5 are true, then the answer is 35, etc. 

1.   Circles F and G are externally tangent.

2.   Circles A and B have exactly two common tangents.

3.   Circles D and E are internally tangent.

4.   Circles F and G have exactly two common internal tangents.

5.   Circles F and G have exactly four common tangents.

6.   Circles F and G have exactly four common external tangents.

7.   Circles H and J have no common internal tangents.

8.   The circles in Figure 2 are internally tangent.

a) 45

b) 36

c) 157

d) 3457

e) 1345678

f) 345

g) None of the above

Answer 1

Hi Amber,

It looks like you only need to understand the associated vocabulary to answer this question. The following link should help: http://jwilson.coe.uga.edu/emt668/emt668.folders.f97/anderson/writeup6/writeup6.html.

Note that for circles to be tangent to each other, they share exactly one common point. However, one may also discuss internal and external tangents (that is tangent lines) to the circles as well.

So circles A and B, and circles D and E are tangent to one another. The only answer options that address this type of tangency, that is, the tangency of the circles themselves are 1 and 3 (I'm not saying whether the statements are true or not, only that they ask about the tangency of the circles.)

All other statements require you to examine how various tangents (that is, tangent lines) could be drawn.

If you still have follow up questions after reading over the material located at the supplied link, I recommend setting up a session to discuss these ideas in more detail.

Regards,

John