SOLUTION: A circle of radius 1 unit has an equilateral triangle PQR inscribed in it. The points S and T are points on the circle such that QRST is a rectangle. Find the area, in square units
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Question 1044489: A circle of radius 1 unit has an equilateral triangle PQR inscribed in it. The points S and T are points on the circle such that QRST is a rectangle. Find the area, in square units, of the rectangle.
I would very much appreciate it if you answered.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
See diagram.
Construct PM perpendicular to RQ
Since PQR is equilateral, ROM must be equilateral, therefore RM measures 1. Since RQ is perpendicular to PM, RQ must bisect angle ORM. Therefore triangle RMN is 30-60-90. So MN measures 1/2, and RN measures 
. RN is half of RQ, so RQ measures 
. RN also bisects OM, so OM must measure 1/2. By symmetrical analysis, OL must measure 1/2.
So the width is 
and the length is , therefore the area is units.
John
My calculator said it, I believe it, that settles it
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