Question 1186394: Please help me with this problem, I would really appreciate it. In ⊙M, chords QR and ST intersect at U. What is TU if QU = 6, RU = 9, and SU = 7?
Answer by ikleyn(52800)   (Show Source):
You can put this solution on YOUR website! .
There is a general theorem in Geometry, saying that
+--------------------------------------------------------------------------+
| if in a circle two chords, QR and ST, intersect at the interior point U |
| |
| of the circle, then QU * RU = SU * TU. |
+--------------------------------------------------------------------------+
In your case, it gives an equation
6 * 9 = 7 * TU.
From this equation, you find TU =  =  = 7  . ANSWER
Solved.
-------------
Regarding this theorem, see the lessons
- The parts of chords that intersect inside a circle
- Solved problems on chords that intersect within a circle,
in this site.
Also, you have this free of charge online textbook on Geometry
GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.
The referred lessons are the part of this online textbook under the topic "Properties of circles, inscribed angles, chords, secants and tangents ".
Save the link to this online textbook together with its description
Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson
to your archive and use it when it is needed.
|
|
|
