SOLUTION: please help me with these questions I'm lost 1. if GM = 5, MJ = 3, and MF = 2, find MH. 2. if LJ = 6, JG = 8, and LI = 7, find IH. 3. if LJ = 3 and JG = 7, find LF. (the im

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Question 1154645: please help me with these questions I'm lost
1. if GM = 5, MJ = 3, and MF = 2, find MH.
2. if LJ = 6, JG = 8, and LI = 7, find IH.
3. if LJ = 3 and JG = 7, find LF.
(the image of the shape is here)
https://photos.google.com/share/AF1QipNDsH-Y-5LCQudqf-ni7jxhbzAdoktuJNcu0JE0nHqluQggBo2jdolV45TQEwTtrw/photo/AF1QipOEDwwcns51zPR9xJdjzFIDEiftO21-uVGDL0Tb?key=WFFkTV82Y2I1VldRRnNfSU92MllTT0czaVA3N3hn
Found 2 solutions by mananth, MathLover1:
Answer by mananth(16949)   (Show Source): You can put this solution on YOUR website!

1. if GM = 5, MJ = 3, and MF = 2, find MH.
GM *MJ = MF * MH ( Property of intersecting chords)
MH = 7.5
2. if LJ = 6, JG = 8, and LI = 7, find IH.
LJ * LG = LI * LH (Intersecting Secants Theorem)
6*14= 7*LH
LH =12
HI = 5

3. if LJ = 3 and JG = 7, find LF.
LJ*LG =LF^2 ( Tangent Secant theorem)
30= lF^2
LF = sqrt(30)

Answer by MathLover1(20855)   (Show Source): You can put this solution on YOUR website!

1. if , , and , find .
When two chords intersect each other inside a circle, the products of their segments are equal.






2. if , , and , find .
If you have a point outside a circle and draw two secant lines (, ) from it, there is a relationship between the line segments formed. Refer to the figure given. If you multiply the length of , you will get the same result as when you do the same thing to the other secant line.

........since , and
we have

.....simplify




3. if and , find.
here is a , so



-> exact solution
-> approximately

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