Which statements are true regarding the relationships between central, inscribed, and circumscribed angles of a circle? Check all that apply.A circumscribed angle is created by two intersecting tangent segments.A central angle is created by two intersecting chords that are not a diameter.The measure of a central angle will be twice the measure of an inscribed angle that intercepts the same arc.The measure of a central angle will be half the measure of an inscribed angle that intercepts the same arc.The measures of a central angle and circumscribed angle that intercept the same arc will sum to 90°.The measure of a central angle will be equal to the measure of an inscribed angle when the arc intercepted by the inscribed angle is twice as large as the arc intercepted by the central angle.
Answer
A
A circumscribed angle is created by two intersecting tangent segments.
B
A central angle is created by two intersecting chords that are not a diameter.
C
The measure of a central angle will be twice the measure of an inscribed angle that intercepts the same arc.
D
The measure of a central angle will be half the measure of an inscribed angle that intercepts the same arc.
E
The measures of a central angle and circumscribed angle that intercept the same arc will sum to 90°.
F
The measure of a central angle will be equal to the measure of an inscribed angle when the arc intercepted by the inscribed angle is twice as large as the arc intercepted by the central angle.
Explanation
A circumscribed angle is formed by two tangent segments that meet outside the circle, so A is true. A central angle has its vertex at the center and is formed by two radii, while an inscribed angle intercepting the same arc measures half the central angle; therefore C is true and D is false. For F, if the inscribed angle intercepts an arc twice the central angle’s arc, its measure is half that arc, making the two angles equal. A central angle and a circumscribed angle intercepting the same arc add to 180°, not 90°.
AI-written and checked against the verified answer.