AnExtremelyLongName

Angle A subtends to arc BC, which is equal to 180. Therefore angle A is 180/2 = 90. Knowing that it is a 45-45-90 triangle, can you figure out the area of the triangle? After that, just subtract it from the area of the semi-circle.

PAB is similar to PDC by AA. The ratio of sides AB:DC is 1:3. That means the ratio of the areas must be 1:9.

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Call the area of PAB \(x\).

 - The area of PDC is obviously \(x+224\)

Since the ratio is 1:9, then we have the following proportion.

 - \(\frac{x}{x+224}=\frac{1}{9}\)

\(x\) is the area of PAB. I leave the rest of the question up to you.

Where is point P?

If your ego and self-esteem comes from flexing your "superior intelligence" on a math forum website then you should be worried and seek help.

Hint: Check if the triangle is a right triangle by seeing if there are slopes that are negative reciprocals.

- Do you know distance formula?

I have cold-like symptoms. Stumbling upon this post makes me scared...

WOAH! If you look at the computer screen, there are beautiful mathematical curves there. If anyone with the knowledge on why the curves look the way they do and their color, it would be very appreciated. I am very curious right now .