Bisectors of Triangles

James and Aria are designing a new park layout. What is the minimum number of pathways that must intersect at a single point to be considered concurrent?

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Find BC.

• BC = 4

• BC = 16

• BC = 12

• BC = 24

Lisa is designing a triangular garden. She wants to place a bench at point D, which is the midpoint of the path from point A to point C. If the length of the path from B to D is given by 2x + 4 and the length from D to A is 4x, find the length of AD.

• 2

• 4

• 6

• 8

Henry, Noah, and Mark are trying to find the best location to place a water fountain in their triangular park. They decide to use the point where the 3 perpendicular bisectors of the park's triangular shape cross. This point is called the ___?

• Midsegment

• Incenter

• Circumcenter

• Centroid

Point O is the circumcenter of the triangle. Find OB

• OB = 4
• OB = 6
• OB = 5.1
• Not enough information

Which of the following describes a perpendicular bisector of a triangle?

• A segment that is perpendicular to the side of a triangle at its midpoint.
• A segment with endpoints at the vertex and midpoint of the opposite side.
• A segment that connects two midpoints of two sides.
• A segment that connects the vertex and the opposite side at 90 degrees. 

• JM = 5

• JM = 10

• JM = 12

• JM = 24

Solve for the value of x.

• x = 10

• x = 20

• x = 3

• x = 45

Point P is the circumcenter, which segment is equal to PB

• DA
• AC
• PC
• PF

The dashed line in the figure is an example of a(n) ...

• angle bisector

• perpendicular bisector

• median

• midsegment