Where is the center of the largest circle that you could draw inside a given triangle?

Question

the point of concurrency of the perpendicular bisectors of the sides of the triangle

the point of concurrency of the altitudes of the triangle

the point of concurrency of the medians of the triangle

the point of concurrency of the angle bisectors of the triangle

Answer 1

The center of the largest circle that you could draw inside a given triangle is the point of concurrency of the angle bisectors of the triangle. This point is known as the **incenter** of the triangle. The incenter is equidistant from all three sides of the triangle, making it the center of the largest possible inscribed circle, or **incircle**.