Question

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.

Explanation:

1. A circumscribed angle is indeed formed by two intersecting tangent segments. This is a standard definition in circle - geometry.
2. A central angle is created by two radii, not two intersecting chords that are not a diameter.
3. The measure of a central angle is twice the measure of an inscribed angle that intercepts the same arc. This is a well - known theorem in circle geometry.
4. The measure of a central angle is not half the measure of an inscribed angle that intercepts the same arc.
5. The measures of a central angle and circumscribed angle that intercept the same arc do not sum to 90°. In fact, they are supplementary in some cases.
6. 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. This is also based on angle - arc relationships in circles.

Answer:

A. A circumscribed angle is created by two intersecting tangent segments.
C. The measure of a central angle will be twice the measure of an inscribed angle that intercepts the same arc.
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.