Among the following, the concurrent lines in a triangle are

Explanation:

• Altitudes: The altitudes of a triangle (lines drawn from each vertex perpendicular to the opposite side) meet at a common point called the orthocenter.
• Medians: The medians of a triangle (lines drawn from each vertex to the midpoint of the opposite side) are concurrent at the centroid, which divides each median into a 2:1 ratio.
• Perpendicular Bisectors: The perpendicular bisectors of the sides of a triangle meet at the circumcenter, the center of the circle that passes through all the triangle's vertices.
• Angle Bisectors: The angle bisectors of a triangle (lines that divide the angles into two equal parts) are concurrent at the incenter, the center of the circle that touches all three sides of the triangle.

Among the options, angle bisectors are specifically concurrent at the incenter of the triangle, which is the point where all three angle bisectors meet. The incenter is equidistant from all three sides of the triangle, making it the center of the triangle's inscribed circle (incircle).

While the other options also describe concurrent lines in a triangle, the question asks for a specific type of concurrency related to angle bisectors, which distinguishes it as the correct answer in this context.