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Is this statement true or falseThe circumcenter of a right triangle always lies on the hypotenuse?
Updated: 12/11/2022
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Is this statement true or falseThe circumcenter of a triangle is the center of its circumscribed circle?
true
Is this statement true or falseThe circumcenter of a triangle is the point of concurrency of the angle bisectors of a triangle?
false
Is this statement true or falseThe cicumcenter of a triangle is always in the interior of a triangle?
false
Is this statement true or falseThe incenter of a triangle is equidistant from the sides of the triangle?
true
Is this statement true or falseThe centroid of a triangle is the point of concurrency of the medians of the triangle?
true
Related questions
Is this statement true or falseThe circumcenter of an obtuse triangle lies inside the triangle?
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Is this statement true or falseThe circumcenter of a triangle is the center of its circumscribed circle?
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Is this statement true or falseThe circumcenter of a triangle is the point of concurrency of the angle bisectors of a triangle?
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Which point of concurrency is always on the midpoint of the hypotenuse in a triangle?
The circumcenter is always on the midpoint of the hypotenuse when it is in a right triangle.
Is this statement true or falseThe cicumcenter of a triangle is always in the interior of a triangle?
false
Is this statement true or falseThe incenter of a triangle is equidistant from the sides of the triangle?
true
Is this statement true or falseThe triangle is a right triangle?
false
Is this statement true or falseThe centroid of a triangle is the point of concurrency of the medians of the triangle?
true
Is this statement true or falseThe center C of the inscribed circle of a triangle is the centroid of the triangle?
false
Is this statement true or falseThe incenter of a triangle is equidistant from all three sides of the triangle?
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Is the centroid of a triangle always the circumcenter of a triangle?
No way! An easy example is the centroid and circumcenter of a right-angle triangle. Circumcenter will be exactly on the middle of the hypotenuse which obviously cannot be the centroid. Centroid is the point where all three lines are connecting all the three vertices and the middle of the line opposite the respective vertex. Circumcenter is the center of the circle passing through all the vertices. As it is known, a right-angle triangle will always fall within a semicircle, meaning the circle center will always be on the middle of the hypotenuse.
Is this statement true or falseThe three perpendicular bisectors of the sides of a triangle are concurrent?
true
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