I normally don't ask multiple questions, but I missed class, and need some help. Any help is appreciated!


1) Three circles are drawn, so that each circle is externally tangent to the other two circles. Each circle has a radius of 2. A triangle is then constructed, such that each side of the triangle is tangent to two circles, as shown below. Find the perimeter of the triangle.



2) The circle with center A and radius 10 and the circle with center B and radius 7 are externally tangent. A line that is externally tangent to both circles is drawn, where both circles lie on the same side of the line. This common tangent intersects line AB  at C  Find the length  BC. 



3) Lines XTQ and XUR are tangent to a circle, as shown below.



If angle ATQ = 41 degrees and angle AUR= 63 degree, then find angle QXR, in degrees.



4) Triangle WXY has side lengths XY=14 and WX=8 . The tangent to the circumcircle of triangle WXY at X is drawn, and the line through W that is parallel to this tangent intersects XY at Z. Find YZ.




Thank you so much!!! laugh



 Jul 31, 2020

For your first question, it has already been answered (by mewink) on this link https://web2.0calc.com/questions/here-s-a-challenge-for-everyone#r5.


Question 2 has also been answered by geno3141 here: https://web2.0calc.com/questions/another-tangent-circle-question-please-explain


Question 3 has been answered by heureka here: https://web2.0calc.com/questions/tangent-question-with-inscribed-angles-please-explain


Question 4 has been answered by Dragan and geusts here: https://web2.0calc.com/questions/help-please-thx_4#r4


(PS, next time, just ask one question at a time, and also, double check to make sure it has not been answered yet, by using the search bar)


By the way, if you missed class, you should always refer to your book or a friend to catch up. This way, you can learn. 

Good luck on your math journey!

 Jul 31, 2020
edited by ilorty  Jul 31, 2020
edited by ilorty  Jul 31, 2020

So sorry! I didn't realize these problems were already answered...


However, question 2 is a bit different than the link you are referring to, maybe it was a mistake?


Question 4's answer was incorrect. Other than those, your solution, and the one for question 3 were very helpful, thank you so much for those!



 Jul 31, 2020

No problem! Let me try the other two problems...

ilorty  Jul 31, 2020

Ok, thank you! smiley

Noori  Jul 31, 2020

Okay.. Here is problem 2.

It seems that the questions matches...maybe you saw the wrong answer? 

But, to save you some time, let me use my language to reword geno's answer. (none of this is my credit, it is all theirs :D, so you should thank them for creating the answer)


Anyways, since the two circles are externally tangent, that means that line AC is 17 degrees. (add the radii) (you can learn more about tangents here: http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Simmons/Assign6/Assign6.html)


Now, since we are looking for BC, we can replace that with a variable, like x.

Using similiar triangles, we see that AX / AC  =  BY / BC, which means 10 / (17 + x)  =  7 / x.

After cross multiplying and simplifying, you will get x  =  119/3


(you could view Post 1 for a more in depth solution)

ilorty  Aug 1, 2020

Oops, I mistook it. Sorry! The answer was correct. (for problem #2)



 Aug 1, 2020
edited by Noori  Aug 1, 2020

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