Question

question 9 of 10

true or false? in order to circumscribe a circle about a triangle, the circles center must be placed at the incenter of the triangle.

a. true
b. false

Explanation:

Define circumscribed circle and its center

Using the Circumscribed Circle and Circumcenter of a Triangle knowledge points

• A circumscribed circle passes through all three vertices of a triangle.
• The center of this circle is the circumcenter, which is the intersection of the perpendicular bisectors of the triangle's sides.

Define inscribed circle and its center

Using the Incenter of a Triangle knowledge point

• An inscribed circle (incircle) is tangent to all three sides of a triangle.
• The center of this circle is the incenter, which is the intersection of the angle bisectors of the triangle.

Compare the centers for circumscribing

Using the Circumcenter of a Triangle and Incenter of a Triangle knowledge points

• To circumscribe a circle about a triangle, the center must be the circumcenter, not the incenter.
• Therefore, the statement is false.

Answer:

• A. True
• B. False (Correct answer)