Question

in jaden’s yard, there is a triangular garden patch. he wants to plant a geranium in the patch at a point equidistant from all its vertices. where should jaden plant the geranium?
a. in the center of the inscribed circle of the triangle
b. in the center of the circumscribed circle of the triangle
c. at the point of intersection of the angle bisectors of the triangle
d. at the point of intersection of an angle bisector and a perpendicular bisector of the triangle

Explanation:

Step1: Recall triangle centers

The circumcenter of a triangle is the point equidistant from all three vertices, as it is the center of the circumscribed (circumcircle) circle that passes through all vertices. The incenter is equidistant from the sides, angle bisectors' intersection is incenter, and angle bisector + perpendicular bisector intersection is not a standard center for equidistance to vertices.

Step2: Analyze options

• Option A: Incenter (equidistant to sides, not vertices).
• Option B: Circumcenter (center of circumcircle, equidistant to vertices).
• Option C: Incenter (intersection of angle bisectors, equidistant to sides).
• Option D: Not a standard center for equidistance to vertices.

Answer:

B. in the center of the circumscribed circle of the triangle