Mathematics

Problem

Let

C

be the circle of minimum area enclosing the ellipse

E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1

with eccentricity

\frac{1}{2}

and foci

(\pm 2, 0)

. Let PQR be a variable triangle, whose vertex

P

is on the circle

C

and the side

QR

of length 29 is parallel to the major axis of

E

and contains the point of intersection of

E

with the negative

y

-axis. Then the maximum area of the triangle PQR is :