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True or false Circles circumscribed about a given triangle will all have centers equal to the incenter but can have different radii?
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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.
The INCENTER of a triangle is the center of the only circle that can be inscribed inside it?
Of course not! There are an infinite number of smaller circles.
The shortest distance from the center of the circumscribed circle to the sides of the inscribed triangle is the circles radius?
FALSE
What is stronger a triangle or a circle?
Circles are a stronger geometrical shape than a triangle. Circles distribute weight equally which makes it more stable. That is why pot holes are circles.
Where must the circles center be placed in an inscribed triangle?
In the middle of the triangle
Circles circumscribed about a given triangle will all have centers equal to the incenter but can have different radii?
Yes, that is correct. Circles circumscribed about a given triangle will have centers that are equal to the incenter, which is the point where the angle bisectors of the triangle intersect. However, the radii of these circles can vary depending on the triangle's size and shape.
How many circumscribed circles can a triangle have?
A triangle has exactly one circumscribed circle.
In order to inscribe a circle in triangle the circles center must be placed at the incenter of the triangle?
That is correct
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.
The INCENTER of a triangle is the center of the only circle that can be inscribed inside it?
Of course not! There are an infinite number of smaller circles.
Is the shortest distance from the center of the circumscribed circle to the vertices of the inscribed triangle is the circles radius?
True
The shortest distance from the center of the circumscribed circle to the sides of the inscribed triangle is the circles radius?
FALSE
How many different inscribed circles can be inscribed in a given triangle?
There is only one possible circle that can be inscribed in any triangle because all of the sides of the triangle must touch the circle at some point. Also, there is only one "incenter" of each circle. The incenter is the center of an inscribed circle.
The shortest distance from the center of the circumscribed circle to the vertices of the inscribed triangle is the circles radius?
False apex q
The center of a regular polygon is the common center for the inscribed and circumscribed circles of the polygon?
Correct.
How do you create three different drawings showing a number of circles and triangles in which the ratio of circles to triangles is 2 to 3?
To create three different drawings showing a number of circles and triangles in which the ratio is 2:3 you can: Start with an equilateral triangle, draw a circle inside it, draw an equilateral triangle inside the circle, draw a circle in the triangle and then draw an equilateral tiangle in the smallest circle. Or, you could draw 3 triangles and 2 circles in a line. Or, you could draw 3 triangles on a line with 2 circles between them.
What is stronger a triangle or a circle?
Circles are a stronger geometrical shape than a triangle. Circles distribute weight equally which makes it more stable. That is why pot holes are circles.
