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 $PQR.$

Area of Triangle QRP = 3

Step-by-step explanation:

According to Question , We have a circle With Centre 'O' & Area 48 .

Area Of Circle = 48

= 48

r =

Now We Have Two Points Given On Circle Q & R , P Is Circumcentre Of Triangle QRO .

Thus A Circle Can Also Be Formed with Centre P . ( See attachment For Diagram )

Now The Diameter of Circle With Centre P = Radius Of Circle with Centre O

so Radius Of Circle With Centre P() =

Now We Have To Find Area Of Equilateral Triangle .

A =

A=

The Area Of PQR is = 3

For Diagram , Please Find In Attachment

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