Drawing Circles Isn't Enough!
Geometry
Level
5
Let \(H\) be the orthocenter of triangle \(ABC\), which has a circumradius of 4.
Let \(P\) be a point on the circumcircle of triangle \(ABC\).
Let \(M\) be the midpoint of \(HP\).
What is the area of the locus enclosed by \(M\) as \(P\) moves along the circumcircle?
Give your answer to 2 decimal places.
Bonus: What specific shape is this locus also known as?
If you think there is no set answer, type 13.37 as your answer.
by
Sharky Kesa