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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

 Jun 3, 2022
 #1
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Hello Nathan,

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

If triangle PQR need not be equilateral, then:

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

laugh  !

 Jun 3, 2022
edited by asinus  Jun 3, 2022
 #2
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Thanks for helping, asinus! However, I checked the answer, and it said that is was incorrect. Furthermore, I do not know where you were wrong.

-Nathan

Guest Jun 4, 2022
 #3
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maybe you have to put in the exact answer, since 3.215 is just an approximation

Guest Jun 4, 2022
 #4
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I did

Guest Jun 4, 2022

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