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.

Thanks! - Nathan

Guest Jun 3, 2022

#1**+1 **

**Hello Nathan,**

if P is the circumcenter of triangle QRO, triangle PQR cannot be equilateral.

If triangle PQR need not be equilateral, then:

\(OQ=OR=QR=\sqrt{\frac{48\pi }{\pi}}=4\sqrt{3}\\ h=tan\ 15°\cdot2\sqrt{3}\\ A_{PQR}=\frac{1}{2} \cdot tan\ 15°\cdot2\sqrt{3}\cdot 4\sqrt{3}\\ \color{blue}A_{PQR}=3.215\)

!

asinus Jun 3, 2022