Question

What is a sketch and description for each locus of points in a plane? The points in the interior of ∠ABC and equidistant from the rays of ∠ABC

Answer 1

The circumcenter (O) is the point in the interior of ∠ABC that's equidistant from all the rays (vertices) of triangle ABC.

What is a locus?

In Geometry, a locus can be defined as a set of points which all meets and satisfies a stated condition for a geometrical figure (shape). This ultimately implies that, the locus of points defines a geometrical figure (shape) in geometry.

What is a circumcenter?

A circumcenter can be defined as the point where perpendicular bisectors (right-angled lines to the midpoint) of the sides of a triangle meet together or intersect.

In this context, we can infer and logically deduce that the circumcenter of any triangle is always equidistant from all the rays (vertices) of that triangle.

In triangle ABC (see attachment), the circumcenter can be determined by drawing the perpendicular bisectors (right-angled lines to the midpoint) of both sides AC and CB.

By critically observing the diagram (see attachment) of these triangles, we can logically deduce that point O is where these perpendicular bisectors meet together or intersect.

In conclusion, the circumcenter (O) is the point in the interior of ∠ABC that's equidistant from all the rays (vertices) of triangle ABC:

OA = OB = OC.

Read more on the locus of points here: brainly.com/question/3678578

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