Question 1095076: Hello. If I have a parallelogram inside a circle, with one corner touching the centerpoint, and 3 corners touching the circle edge, how can I calculate the angles of the parallelogram without having any given angle in the question? This question is from a school book. Thank you.
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
If a parallelogram has one vertex at the center of a circle and the other three vertices on the circle, then two adjacent sides of the parallelogram are the same length; that means the parallelogram is a rhombus.
In fact, the rhombus has to be one with angles of 60 and 120 degrees.
If you have trouble visualizing that (I did!), inscribe a regular hexagon ABCDEF in circle O and draw radii OA, OC, and OE....
So a parallelogram with the specified conditions has to be a rhombus with angles of 60 and 120 degrees.
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