Question 180509
 X=({{{sqrt(45))}}},{{{ 2*sqrt(18)}}})=(6.7,8.5)
Y=({{{7*sqrt(5) }}},{{{ -3*sqrt(2) }}}) =(15.7,-4.3)
Z=({{{sqrt(5) }}},{{{ -sqrt(2) }}})=(2.2,-1.4)

Frist find the midpoint of YZ.
{{{x[m]=(x[Y]+x[Z])/2}}}
{{{x[m]=(7*sqrt(5)+sqrt(5))/2}}}
{{{x[m]=(8*sqrt(5))/2}}}
{{{x[m]=4*sqrt(5)}}}
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{{{y[m]=(-3*sqrt(2)+(-sqrt(2)))/2}}}
{{{y[m]=(-4*sqrt(2))/2}}}
{{{y[m]=-2*sqrt(2)}}}
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 X=({{{sqrt(45))}}},{{{ 2*sqrt(18)}}})
Y=({{{7*sqrt(5) }}},{{{ -3*sqrt(2) }}}) 
Z=({{{sqrt(5) }}},{{{ -sqrt(2) }}})
M=({{{4*sqrt(5) }}},{{{ -2*sqrt(2) }}})
{{{drawing( 300, 300, -2, 18, -8, 12,grid( 1 ),
circle( sqrt(45), 2*sqrt(18), .4 ),
circle( 7*sqrt(5) ,-3*sqrt(2), .4 ),
circle( sqrt(5),-sqrt(2),.4 ),
circle( 4*sqrt(5),-2*sqrt(2),.4 ),
line( 4*sqrt(5),-2*sqrt(2),sqrt(45),2*sqrt(18) ),
locate(7.2,9.5,X),
locate(16.2,-4.2,Y),
locate(1.2,-1.5,Z),
locate(9,-3,M),
green(line( 7*sqrt(5) ,-3*sqrt(2),  sqrt(5),-sqrt(2))))}}}
Now use the distance formula,
{{{D=sqrt((x[x]-x[m])^2+(y[x]-y[m])^2)}}}
{{{D=sqrt((sqrt(45)-4*sqrt(5))^2+(2*sqrt(18)-(-2*sqrt(2)))^2)}}}
{{{D=sqrt((3*sqrt(5)-4*sqrt(5))^2+(2*3*sqrt(2)+2*sqrt(2))^2)}}}
{{{D=sqrt((-sqrt(5))^2+(8*sqrt(2))^2)}}}
{{{D=sqrt(5+128)}}}
{{{D=sqrt(133)}}}