Question 1195534


if the point ({{{3}}},{{{2}}}) is the midpoint of a chord and centre ({{{2}}},{{{ 4}}}),  the distance of the chord from the centre is equal to the distance between centre ({{{2}}}, {{{4}}}) and  the point ({{{3}}},{{{2}}}) 

{{{d=sqrt((3-2)^2+(2-4)^2)}}}

{{{d=sqrt(1+4)}}}

{{{d=sqrt(5)}}}

the distance of the chord from the centre is {{{sqrt(5)}}}



the length of the chord:

midpoint of the chord, center and endpoint of the chord for right triangle 

one leg is {{{d=sqrt(5)}}}, hypotenuse is radius {{{r=5}}}, and other leg is a half the length of the chord

so, let the length of the chord be {{{c}}}

then {{{c=sqrt(r^2-d^2)}}}

{{{c=sqrt(5^2-sqrt(5)^2)}}}

{{{c=sqrt(25-5)}}}

{{{c=sqrt(20)}}}

{{{c=sqrt(4*5)}}}

{{{c=2sqrt(5)}}}

the length of the chord is {{{2sqrt(5)}}}