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
+14915 Hello Nathan,
if P is the circumcenter of triangle QRO, triangle PQR cannot be equilateral.
If triangle PQR need not be equilateral, then:
\(OQ=OR=QR=\sqrt{\frac{48\pi }{\pi}}=4\sqrt{3}\\ h=tan\ 15°\cdot2\sqrt{3}\\ A_{PQR}=\frac{1}{2} \cdot tan\ 15°\cdot2\sqrt{3}\cdot 4\sqrt{3}\\ \color{blue}A_{PQR}=3.215\)
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