MathDB

Let

C

be a closed plane curve that has a continuously turning tangent and bounds a convex region. If

T

is a triangle inscribed in

C

with maximum perimeter, show that the normal to

C

at each vertex of

T

bisects the angle of

T

at that vertex. If a triangle

T

has the property just described, does it necessarily have maximum perimeter? What is the situation if

C

is a circle?

Problem Statement