1. Let P be the centroid of triangle ABC. If triangle ABP is an equilateral triangle with a side length of 2, then find the perimeter of triangle ABC.


2. In triangle PQR, the side lengths are PQ = 9, PR = 10, and QR = 17. Let X be the intersection of the angle bisector of angle P with side QR, and let Y be the foot of the perpendicular from X to side PR. Compute the length of side XY.


 3. A circle is centered at O and has an area of 48pi. Let Q and R be points on the circle, and let P be the circumcenter of triangle QRO. If P is contained in triangle QRO, and triangle PQR is equilateral, then find the area of triangle PQR.


4. In triangle ABC, point P is on side BC such that PA = 13, PB = 14, PC = 4, and the circumcircles of triangles APB and APC have the same radius. Find the area of triangle ABC.

 Mar 19, 2020

Hey fellow AoPSer! Here are the ones I've solved so far. (Ur prob on a different class but whatever)

1. 4sqrt7+2 (aops will convert it to latex automatically)


2. 72/19


3. 24sqrt3-36


4. idk still stuck :((((

 Mar 30, 2020

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