Question 1154645


1. if {{{GM = 5}}}, {{{MJ = 3}}}, and {{{MF = 2}}}, find {{{MH}}}.

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

{{{GM *MJ=MH*MF}}}

{{{5*3=MH*2}}}

{{{15=MH*2}}}

{{{MH=15/2}}}

{{{MH=7.5}}}


2. if {{{LJ = 6}}}, {{{JG = 8}}}, and {{{LI = 7}}}, find {{{IH}}}.

 If you have a point {{{L}}} outside a circle and draw two secant lines ({{{LJG}}}, {{{LIH}}}) from it, there is a relationship between the line segments formed. Refer to the figure given. If you multiply the length of {{{LJ by the length of {{{LG}}}, you will get the same result as when you do the same thing to the other secant line.


{{{LJ*LG = LI*LH}}}........since {{{LG=LJ+JG = 6+8=14}}}, and {{{LH= LI+IH=7+IH}}}

we have

{{{6*14 = 7*(7+IH)}}}

{{{7+IH=(6*14)/7}}}.....simplify

{{{7+IH=6*2}}}

{{{IH=12-7}}}

{{{IH=5}}}


3. if {{{LJ = 3}}} and {{{JG = 7}}}, find{{{ LF}}}.

here {{{LF}}} is a {{{tangent}}}, so

{{{LF^2=LJ*JG}}}

{{{LF^2=3*7}}}

{{{LF^2=21}}}

{{{LF=sqrt(21)}}}-> exact solution

{{{LF=4.6}}}-> approximately