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The circumcenter of a triangle is the center of the only circle that can be circumscribed about it?
True
The of a triangle is the center of the only circle that can be inscribed inside it?
incenter
The incenter of a triangle is the center of the only circle that can be inscribed in it?
true
If orthocentre and circumcentre of a triangle coincide then is it an equilateral triangle?
Yes. The orthocenter is the intersection of the altitudes; the circumcenter is the intersection of the perpendicular bisectors of the three sides of the triangle. The perpendicular bisector of and altitude to a given side are parallel, so they can coincide at the common center only if they are the same; that means that the opposite vertex is on the perpendicular bisector, so the other two sides are equal. Thus each pair of sides are equal, so the triangle is equilateral.
What does an inverted triangle inside of a circle mean?
It means just what is written. It is an image that contains both a circle and in inverted triangle. The inverted triangle is inside the circle. See below for an triangle examples. Below is a "normal triangle" has a wide base on the bottom of the image: (Disregard the "." characters. They are only there for spacing purposes.) ......./\ ....../_\ ...../__\ ..../___\ .../____\ ../_____\ ./______\ /_______\ Below is an "inverted triangle" has a wide base on the top of the image: (Disregard the "." characters. They are only there for spacing purposes.) _________ \ _______/ .\______/ ...\____/ ... \___/ ......\_/ .......\/
