Q: If a circle is circumscribed around a triangle then how many of the triangle's vertices must it pass through?

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Centre of area of a triangle is the centre point for a circumscribed radius which will pass through all 3 vertices of the triangle.

It is called the circumcenter of the triangle. . The circumcenter is equidistant from the three vertices, and so the common distance is the radius of a circle that passes through the vertices. Another name for it is the circumcircle

equidistant from the vertices

circumcircle of a triangle is the circle that passes through all 3 vertices. this circle is said to be circumscribe the triangle

The triangle that has all three vertices touching the circle is called an 'inscribed triangle.' The circle has no special name, only the polygon inscribed.

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Centre of area of a triangle is the centre point for a circumscribed radius which will pass through all 3 vertices of the triangle.

It is called the circumcenter of the triangle. . The circumcenter is equidistant from the three vertices, and so the common distance is the radius of a circle that passes through the vertices. Another name for it is the circumcircle

It is the circumcentre, the unique point from which you can draw a circle (the circumscribed circle) which passes through all three vertices.

It is the circumcentre, the unique point from which you can draw a circle (the circumscribed circle) which passes through all three vertices.

They are lines, through the vertices of a triangle, that bisect (divide into two halves) the angles of the triangle.

equidistant from the vertices

circumcircle of a triangle is the circle that passes through all 3 vertices. this circle is said to be circumscribe the triangle

The circumscribing circle.

The triangle that has all three vertices touching the circle is called an 'inscribed triangle.' The circle has no special name, only the polygon inscribed.

Circumcenter - the center of the circle that circumscribes the triangle, ie. goes through all its vertices.

If one of the three interior angles is 90 degrees then it is a right triangle.

Yes, midway.