If the point is the same distance from the two objects then it is

Equidistant

The length of the perpendicular segment from the point to the line

Distance from a point to a line

When three or more lines intersect at one point they are

Concurrent

The point at which they intersect

Point of concurrency

The point of concurrency of the perpendicular bisectors of a triangle

Circumcenter of the triangle

Since the circumcenter is equidistant from the vertices, you can use the circumcenter as the center of the circle that contains each vertex of the triangle

Circumscribed about

The point of concurrency of the angle bisectors of a triangle

Incenter of the triangle

The letter in the center of the circle

Inscribed in

A segment whose endpoints are a vertex and the midpoint of the opposite side

Median of a triangle

The point of concurrency of the medians

Centroid of the triangle

The perpendicular segment from a vertex of the triangle to the line containing the opposite side

Altitude of a triangle

The lines that contain the altitudes of a triangle are concurrent at the

Orthocenter of the triangle

All possibilities are considered and then all but one are proved false

Indirect reasoning

A proof involving indirect reasoning is an

Indirect proof

A segment connecting the midpoints of two sides of the triangle

Midsegment of a triangle