Question

part c with point d as the center, create a circle passing through point e. measure the radius of the inscribed circle. would the radius be different if you used a line perpendicular to bc instead of ab to create the circle? explain your reasoning. since point d is the center of the circle that will be inscribed, and the inscribed circle will intersect ab at point e, ab is tangent to the inscribed circle. since de is perpendicular to tangent ab, de is the radius of the largest circle that will fit within triangle abc. hide sample answer

Explanation:

The radius of an inscribed - circle in a triangle is determined by the distance from the in - center (point D) to the point of tangency (e.g., E). The in - center is equidistant from all sides of the triangle. Changing the side to which the perpendicular is drawn from the in - center does not change the radius of the inscribed circle because the in - center's property of being equidistant from all sides remains the same.

Answer:

No, the radius would not be different. The in - center of a triangle is equidistant from all sides of the triangle. So, whether we draw a perpendicular from the in - center to AB or BC, the length of the perpendicular (which is the radius of the inscribed circle) remains the same due to the in - center's property of being the center of the circle tangent to all three sides of the triangle.