Question

question 1 of 1

true or false? the shortest distance from the center of the circumscribed circle to the vertices of the inscribed triangle is the circles radius.

a. true
b. false

Explanation:

Define the geometric terms

Using the Circle Definitions knowledge point

• A circumscribed circle (or circumcircle) is a circle that passes through all the vertices of a polygon.
• An inscribed triangle is a triangle whose vertices all lie on the circumscribed circle.

Determine the distance to the vertices

Using the Radius of a Circle knowledge point

• By definition, every point on a circle is at an equal distance from the center.
• This constant distance from the center to any point on the circle is the radius \(R\).
• Since the vertices of the inscribed triangle lie on the circle, the distance from the center to each vertex is exactly \(R\).
• Thus, the distance is constant, making the "shortest distance" exactly equal to the radius.

Evaluate the statement

• The statement says: "The shortest distance from the center of the circumscribed circle to the vertices of the inscribed triangle is the circle's radius."
• Since the distance to every vertex is exactly the radius, the statement is true.

Answer:

• (A) True (Correct answer)
• (B) False