Question 1012679
STEP 1: Find intersection points of secant line and circle.
(solve simultaneous equations by substitution)
.
{{{y=x}}}  
{{{x^2+y^2-6x-8y+9=0}}} . Substitute for y (y=x)
{{{x^2+y^2-6x-8x+9=0}}}
{{{2x^2-14x+9=0}}}
.
*[invoke quadratic "x", 2, -14, 9 ]
.
x=6.28388218141501 --OR-- x=0.716117818584989
. 
Since y=x, the endpoints of the secant segment are:
({{{x[1]}}},{{{y[1]}}})=(6.28388218141501, 6.28388218141501)
({{{x[2]}}},{{{y[2]}}})=(0.716117818584989, 0.716117818584989)
. 
STEP 2: Find the distance between the points:
.
{{{distance=sqrt((x[2]-x[1])^2+(y[2]-y[1])^2)}}}
.
{{{distance=sqrt((0.72-6.28)^2+(0.72-6.28)^2)}}}
.
{{{distance=sqrt(2(-5.56)^2)}}}
.
{{{distance=sqrt(2)5.56}}}={{{7.86}}}( {{{approx}}})
.
{{{ graph( 800, 800, -10, 10, -10, 10, y=x, 
sqrt(16-(x-3)^2)+4, -sqrt(16-(x-3)^2)+4 ) }}}
.
I don't know why there is a gap in the circle. It shouldn't be there.