The sign of the Deathly Hallows is shown below:
A picture of it appears on p. 405 in the seventh Harry Potter book by J.K. Rowling, Harry Potter and the Deathly Hallows. The sign is an isosceles triangle with a circle inscribed in it and an altitude drawn from the vertex angle.
If the base of the triangle is six inches long and the altitude is four inches long, what is the area of the circle?
Solution to the Problem:
The area of the circle is 
square inches, which is
approximately 7.07 square inches.
Triangle AED is isosceles with EA = AD.
From geometry, we know that BD = DF = EF = 3 inches.
We also know that triangle ABC is a right triangle, as is triangle AFD.
In triangle AFD, FD = 3 and AF = 4.
Using the Pythagorean Theorem, AD = 5.
Since BD = 3, then AB = 2.
Let x = length of the radius of the circle.
Then AC = 4 - x.
Using the Pythagorean Theorem in triangle ABC,
(4 - x)2 = 22 + x2
16 - 8x + x2 = 4 + x2
So, 8x = 12 and the radius x = 3/2 inches.
Therefore the area of the circle is square inches.
Correctly solved by:
| 1. K. Sengupta | Calcutta, INDIA |
| 2. Les Walker | Ventura, California |
| 3. John Funk | Ventura, California |
| 4. Richard K. Johnson | La Jolla, California |