Online Course Discussion Forum

MC I-C Geometry 6.23/24/28/30

 
 
Picture of Alex Ye
MC I-C Geometry 6.23/24/28/30
by Alex Ye - Monday, January 29, 2024, 7:56 PM
 

I'm not sure how to write the proof for problems 6.23 and 6.24, and I need the solutions for 6.28 and 6.30. Thank you!

 
Picture of Dr. Kevin Wang
Re: MC I-C Geometry 6.23/24/28/30
by Dr. Kevin Wang - Tuesday, January 30, 2024, 6:03 PM
 

6.23 is another case of the problem in 6.3.  Try to understand the proofs in 6.3(a) and 6.3(b), and use a similar idea to 6.3(b) to work on 6.23.

6.24 is similar to 6.4.

In most chapters, there are the similarity between the practice problems and the example problems of corresponding problem numbers like the above.

For 6.28 and 6.30, they are not exactly similar to the problems 6.8 and 6.10.  One first thing to do for the problems is to draw the diagrams.  Interpret the question in an accurate diagram, and see what is known and what is to be found.  Some auxiliary lines could be added.  The general guidelines include: if two circles are tangent to each other, connect their centers (the line will pass through the tangent point); if one circle and one line are tangent, make a radius connecting the center and the tangent point (the radius is perpendicular to the given line). 

Picture of Alex Ye
Re: MC I-C Geometry 6.23/24/28/30
by Alex Ye - Tuesday, January 30, 2024, 9:16 PM
 
For 6.28, my answer is 26, and I can't think how I got this wrong. Can you see if it's correct?

For 6.30, I found that the answer is 20. I saw the wrong shortest line segment PQ that is tangent to both circles.

Thank you!

Picture of John Lensmire
Re: MC I-C Geometry 6.23/24/28/30
by John Lensmire - Monday, February 5, 2024, 10:18 AM
 

Hi Alex, thanks for your patience with our reply back.

6.28 should actually be 26, but 20 is correct for 6.30. For 6.28, since the circles are of different sizes, one can fit "under" the other a little bit.

One note in case it's unclear: You can also review your homework after it is graded on the course page. Click on the assignment again, then choose "Review". Then you can see both the grader comments as well as the answers and solution ideas for most of the problems. That can then be an additional way to check your answers after you review the problems a bit as well. Note: We're still happy to answer questions or clarifications you need on the forum, just wanted to make sure you knew about reviewing the homework as well!