SOLUTION: Help with angles in circles! Here's a picture: https://imgur.com/prybHbW Here are my questions: 1. If AF = 8, FB = 6, FG = 2, then what is EF? 2. If BC = 12 and GC = 6,

Question 1116742: Help with angles in circles!
Here's a picture:
https://imgur.com/prybHbW
Here are my questions:
1. If AF = 8, FB = 6, FG = 2, then what is EF?

2. If BC = 12 and GC = 6, what is EG?
3. What is the length of a segment whose endpoints are at (-1,4) and (3,1)?
I think I'm doing the wrong formulas to get my answer. Please help!
Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website!
.
I will answer question 1 only.

Use the Theorem:

    If two chords intersect in the interior of a circle,  then the product the measures of the segments the intersection point 
    divides each chord is the same.

    See the lesson     - The parts of chords that intersect inside a circle in this site. 


Then you have  |AF|*|BF| = |EF|*|GF|,   or   8*6 = 2*|EF|,   which implies

|EF| =  = 24 units.

Solved.

-------------------
In this site, you have this free of charge online textbook on Geometry
GEOMETRY - YOUR ONLINE TEXTBOOK

The referred lesson is 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.

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