A circle with radius $5$ and center $(a,b)$ is tangent to the lines $y = 6$ and $y = x.$ Compute the largest possible value of $a + b.$
Hello Guest!
y = 6
y = x
P(6,6)
mf(x)=tan22.5∘f(x)=m(x−xP)+yPf(x)=tan 22.5∘(x−6)+6f(x)=tan 22.5∘⋅x−6⋅tan 22.5∘+6f(x)=tan 22.5∘⋅x+6(1−tan 22.5∘)
g(x)=6−5=1g(x)=f(x)1=tan 22.5∘⋅x+6(1−tan 22.5∘)x=1−6(1−tan 22.5∘)tan 22.5∘x=a=−6.071y=b=1a+b=−5.071
!
!
