Question 1179512
A circle has a centre of ({{{0}}},{{{0}}}) and a radius of {{{13}}}.

Draw a circle with a centre of ({{{0}}},{{{0}}}) and a radius of {{{13}}}.  

You may use Geogebra for this assignment, or some other graphing software, or you may draw the graph by hand on graph paper.

using formula

{{{x^2+y^2=13^2}}}

{{{x^2+y^2=169}}}


{{{ graph( 600,600, -15, 15, -15, 15,- sqrt(-x^2+169) ,sqrt(-x^2+169)) }}}


The points A(0, _ ) , B( _ ,0) and C( _, _ ) are points on the circle. 

From your graph, determine a possible value to fill in each blank for each point. The point C must not contain any zeroes in its coordinates.
Construct the chords AB and AC.

A(0, 13 ) , B( 13 ,0) and C( 0, 0 )

{{{ drawing( 600,600, -15, 15, -15, 15,
circle(0,13,.13), locate(0.3,13,A(0,13)),
circle(13,0,.13), locate(12,0.7,B(13,0)),
green(line(0,13,13,0)), green(line(0.2,13,0.2,0)), 
graph( 600,600, -15, 15, -15, 15,- sqrt(-x^2+169) ,sqrt(-x^2+169))) }}}

Construct the perpendicular bisectors of the chords.
the perpendicular bisector of {{{AC}}} is a line {{{y=13/2=6.5}}} and the perpendicular bisector of {{{AB}}} is a line {{{y=x}}}


{{{ drawing( 600,600, -15, 15, -15, 15,
circle(0,13,.13), locate(0.3,13,A(0,13)),
circle(13,0,.13), locate(12,0.7,B(13,0)),
green(line(0,13,13,0)), green(line(0.2,13,0.2,0)), 
graph( 600,600, -15, 15, -15, 15,- sqrt(-x^2+169) ,sqrt(-x^2+169),x,13/2)) }}}


Construct the intersection of the perpendicular bisectors of the chords. Where do the bisectors intersect?

the bisectors are {{{y=13/2=6.5}}}  and {{{y=x}}} 

if 
{{{y=6.5}}}
{{{y=x}}}

=>{{{x=6.5}}}

the bisectors intersect at ({{{6.5}}},{{{6.5}}})



{{{ drawing( 600,600, -15, 15, -15, 15,
circle(0,13,.13), locate(0.3,13,A(0,13)),
circle(13,0,.13), locate(12,0.7,B(13,0)),
green(line(0,13,13,0)), green(line(0.2,13,0.2,0)), 
circle(6.5,6.5,.13), locate(6.5,6.5,p(6.5,6.5)),

graph( 600,600, -15, 15, -15, 15,- sqrt(-x^2+169) ,sqrt(-x^2+169),x,13/2)) }}}