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# Geometry

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Hi everyone!  This is a problem from the last class of my geometry course, and I am a bit stuck on it.  The week focus is "challenging problems", so I know that it is meant to be hard and I just need a hint to get started, because I don't know how to.  Thank you in advance!

A circle is centered at O and has an area of 48*pi. 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.

Jun 22, 2020

#1
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As an equilateral triangle, the area of triangle PQR works out to 48*sqrt(3).

Jun 22, 2020
#2
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Could you explain to me how you got that answer?

Jun 22, 2020
#3
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Using this diagram, you should be able to find the area of the equilateral triangle QRP.

Area of a triangle QRP = 3√3

Jun 22, 2020
edited by Dragan  Jun 22, 2020
edited by Dragan  Jul 24, 2020
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Thank you!! I got it!

ConfuzzledKitten  Jun 23, 2020