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Shkiper50 [21]
3 years ago
7

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 circumcente

r of triangle $QRO.$ If $P$ is contained in triangle $QRO,$ and triangle $PQR$ is equilateral, then find the area of triangle $PQR.$
Mathematics
1 answer:
nikklg [1K]3 years ago
7 0

Answer:

Area of Triangle QRP = 3\sqrt{3}

Step-by-step explanation:

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

Area Of Circle = 48\pi

\pir^{2} = 48\pi

r = \sqrt{48}

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(r_{2}) = \frac{\sqrt{48}}{2}

Now We Have To Find Area Of Equilateral Triangle .

A = \frac{\sqrt{3}}{4} r_{2} ^{2}

A= \frac{\sqrt{3} }{4} * \frac{\sqrt{48} }{2}*\frac{\sqrt{48} }{2}

The Area Of PQR is = 3\sqrt{3}

For Diagram , Please Find In Attachment

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