37.Where is the incenter of any given triangle ?38. Which of the following describes a median of a triangle ?

Answer:

Part 1) Option The point of concurrency of the angle bisectors of the triangle

Part 2) Option A segment drawn  from a vertex to the midpoint of the opposite side

Step-by-step explanation:

Part 1)

we know that

The incenter is the point where the angle bisectors intersect. The incenter is also the center of the triangle's incircle.

therefore

Is the point of concurrency of the angle bisectors of the triangle

Part 2)

we know that

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side

therefore

Is a segment drawn  from a vertex to the midpoint of the opposite side

Final answer:

The incenter of a triangle is the point where the angle bisectors intersect, and it is equidistant from the three sides. A median of a triangle is a line segment connecting a vertex to the midpoint of the opposite side. The medians meet at a point called the centroid.

Explanation:

The incenter of a triangle is the point where the angle bisectors intersect. It is equidistant from the three sides of the triangle. To find the incenter, you can use the formula:

incenter = (ax + bx + cx) / (a + b + c)

where (ax, ay), (bx, by), and (cx, cy) are the coordinates of the triangle's vertices, and a, b, and c are the lengths of the sides opposite to the vertices, respectively.

A median of a triangle is a line segment connecting a vertex to the midpoint of the opposite side. It divides the triangle into two equal areas. The medians of a triangle meet at a point called the centroid.

Learn more about Triangle Incenter and Median here:

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