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.

The answer is not 3sqrt3!

ianw11 Dec 22, 2020

#1**0 **

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.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

OQ = OR = r = 4√3

∠QOR = 30º ∠QOP = 15º ∠QPR = 60º

QR = 2 (OQ * sin∠QOP) ==> QR = 6*sqrt(3)

Height of ΔPQR h = sqrt[PQ2 - (QR/2)2] = 12*sqrt(3)

[PQR] = h * QR / 2 = 8*sqrt(3)

Guest Dec 23, 2020

#2**+1 **

Just a quick question, how did you form the equations QR = 2 (OQ * sin∠QOP) and h = sqrt[PQ2 - (QR/2)2] = 12*sqrt(3)?

ianw11
Dec 23, 2020

#3**+3 **

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.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

OQ = OR = r = 4√3

∠QOR = 30º ∠QOP = 15º ∠QPR = 60º

QR = 2 (OQ * sin∠QOP) ==> QR = 3.586301889

Height of ΔPQR h = sqrt[PQ^{2} - (QR/2)^{2}] = 3.105828542

**[PQR] = 1/2(h * QR) = 5.569219383 u ^{2}**

jugoslav
Dec 23, 2020

#6**+1 **

Why have you asked this same question twice in two days you little ##@%##$%#@@# ?

You have 9 answers on one thread and 5 on the other.

You are totally out to waste everybody's time!

And jugoslav, why have you fully answered on both threads without even commenting?

Melody Dec 23, 2020

#10**+1 **

Here I wanted to correct answer #1. I copied and pasted the whole answer and have corrected what was wrong.

I apologize if I've done something wrong, teacher.

Guest Dec 23, 2020

#12**0 **

I am only on as a guest because i tried to register for an account at the end it said to check my email for account conformation or something and i did but there was nothing in my email and when i tried to log in it said invalid username or password......

-Grace

Guest Dec 24, 2020