April 13th, 2017, 08:42 AM  #1 
Senior Member Joined: Apr 2017 From: New York Posts: 128 Thanks: 6  tangent lines and chords
Hello everyone, I have a question that I couldn't solve guys. Will you please help me to find x value and explain why? I really appreciate. LEO PS: I read all about tangent lines and chords but couldn't find which theorem is related with this. 
April 13th, 2017, 08:49 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,837 Thanks: 1479 
What can you say about the 4 triangles shown?

April 13th, 2017, 09:46 AM  #3 
Senior Member Joined: Apr 2017 From: New York Posts: 128 Thanks: 6 
congruent?

April 13th, 2017, 09:47 AM  #4 
Senior Member Joined: Apr 2017 From: New York Posts: 128 Thanks: 6 
so x will be 8 ?

April 13th, 2017, 09:53 AM  #5 
Senior Member Joined: Apr 2017 From: New York Posts: 128 Thanks: 6 
is my numbers on the lines correct then?

April 13th, 2017, 10:42 AM  #6 
Math Team Joined: Jul 2011 From: Texas Posts: 2,837 Thanks: 1479  
April 13th, 2017, 11:25 AM  #7 
Senior Member Joined: Apr 2017 From: New York Posts: 128 Thanks: 6 
This is the question. no other explanation. and the answer supposed to be 16. I understood the way you explained perfectly but the answers are not matching with my geometry book and no sample question nor explanation. thanks a lot. 
April 13th, 2017, 11:50 AM  #8 
Math Team Joined: Jul 2011 From: Texas Posts: 2,837 Thanks: 1479 
misinterpretation that the entire chord length is 8 ... only half of the chord has length 8, ergo 16 is the entire chord length
Last edited by skeeter; April 13th, 2017 at 12:07 PM. 
April 13th, 2017, 12:35 PM  #9 
Senior Member Joined: Apr 2017 From: New York Posts: 128 Thanks: 6 
Ok. Got you. Thanks a lot.

April 13th, 2017, 12:54 PM  #10 
Senior Member Joined: Apr 2017 From: New York Posts: 128 Thanks: 6 
and here how am I going to continue to find x as 5?


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chords, lines, tangent 
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