________ is the point at which the perpendicular bisectors of the sides meet and the center of the circle that circumscribes the triangle is _________.

Options

A. Incenter, Circumcenter
B. Circumcenter, Circumcenter
C. Circumcenter, Incenter
D. Orthocenter, Circumcenter

Answer

To solve the question, we need to identify two key concepts related to triangles: the point where the perpendicular bisectors of the sides meet and the center of the circle that circumscribes the triangle.

### Step-by-Step Solution:

1. **Understanding the Triangle**:
- We start by considering a triangle, which we can label as triangle ABC.

2. **Drawing the Perpendicular Bisectors**:
- For each side of the triangle (AB, BC, and CA), we need to draw the perpendicular bisector.
- The perpendicular bisector of a line segment is a line that is perpendicular to the segment and divides it into two equal parts.

3. **Finding the Intersection Point**:
- The three perpendicular bisectors will intersect at a single point.
- This point is significant because it is equidistant from all three vertices of the triangle.

4. **Identifying the Point**:
- The point where the perpendicular bisectors meet is known as the **circumcenter** of the triangle.

5. **Circumscribing Circle**:
- A circle can be drawn with the circumcenter as the center and the distance from the circumcenter to any vertex as the radius.
- This circle is known as the circumcircle, and it touches all three vertices of the triangle.

6. **Filling in the Blanks**:
- Therefore, the answers to the blanks in the question are both "circumcenter".

### Final Answer:
- The point at which the perpendicular bisectors of the sides meet is the **circumcenter**.
- The center of the circle that circumscribes the triangle is also the **circumcenter**.