Question

question 3 of 10

the shortest distance from the center of the inscribed circle to the triangles sides is the circles ______.

a. radius
b. diameter
c. circumference
d. incenter

Explanation:

Define the inscribed circle

An inscribed circle (or incircle) of a triangle is a circle that is tangent to all three sides of the triangle.

Analyze the shortest distance

Using the Tangent Line and Tangent-Radius Theorem knowledge points:
The sides of the triangle are tangent lines to the inscribed circle. The shortest distance from a point (the center) to a line (a side) is the perpendicular segment from the point to the line.

Identify the segment

Using the Radius of a Circle and Circle Definitions knowledge points:
The perpendicular segment from the center of the circle to any point of tangency on a side is a radius of the circle.

Select the correct option

The shortest distance from the center of the inscribed circle to the triangle's sides is the circle's radius (also known as the inradius).

Answer:

• A. radius (Correct answer)
• B. diameter
• C. circumference
• D. incenter