MathDB

In the figure below, points

A

B

, and

C

are distance 6 from each other. Say that a point

X

is reachable if there is a path (not necessarily straight) connecting

A

and

X

of length at most 8 that does not intersect the interior of

\overline{BC}

. (Both

X

and the path must lie on the plane containing

A

B

, and

C

.) Let

R

be the set of reachable points. What is the area of

R

? [asy] unitsize(40); pair A = dir(90); pair B = dir(210); pair C = dir(330); dot(A); dot(B); dot(C); draw(B -- C); label("

A

", A, N); label("

B

", B, W); label("

C

", C, E); [/asy]

Problem Statement