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The circle's center must be placed at the incenter of the triangle?
No, there are two circles (incircle, circumcircle) associated with triangles and in general the locations of their centres are different.
In order to circumscribe a circle in a triangle the circle's center must be placed at the center of the triangle?
Yes, but which centre: the centroid, incentre or orthocentre? You need the incentre.
What is the use of concentric circles?
The use of concentric circles is most commonly used on a target. Concentric circles are placed around a target in which each concentric circle has the same center.
What number do you get placing digits 1 to 7 in circles?
That depends upon how the circles are located and the relationship between the numbers that are placed in the circles; unless the circles just happen to make a number, for example: .............. ..O.O.O.... ..........O.. ........O.... ......O...... ....O........ is a 7 regardless of what digits are placed in the circles.
How do you put 1 to 11 into circles so that every line is the same total?
That depends how the circles are placed on the page and what lines are defined between the circles.
