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true
150
½ the sum of the intercepted arcs.
40, 100 and 83, 143.
72
It is the measure of half the intercepted arc.
true
150
4/9*pi*r where r is the radius of the circle.
True
In a circle, a central angle is formed by two radii. By definition, the measure of the intercepted arc is equal to the central angle.
Examples to show how to use the property that the measure of a central angle is equal to the measure of its intercepted arc to find the missing measures of arcs and angles in given figures.
The measure of the angle formed by two secants intersecting outside the circle is one-half the difference of the intercepted arcs. Example: Major intercepted arc is 200o and the minor intercepted arc is 120o. 1/2 (200-120) = 40o ... The measurement of the angle formed by the two secants is 40o. I HOPE THIS CAN HELP YOU :))
½ the sum of the intercepted arcs.
40, 100 and 83, 143.
72
It is true that the measure of a tangent-chord angle is half the measure of the intercepted arc inside the angle. When a tangent line intersects a chord of a circle, it creates an angle between the tangent line and the chord, known as the tangent-chord angle. If we draw a segment from the center of the circle to the midpoint of the chord, it will bisect the chord, and the tangent-chord angle will be formed by two smaller angles, one at each end of this segment. Now, the intercepted arc inside the tangent-chord angle is the arc that lies between the endpoints of the chord and is inside the angle. The measure of this arc is half the measure of the central angle that subtends the same arc, which is equal to the measure of the angle formed by the two smaller angles at the ends of the segment that bisects the chord. Therefore, we can conclude that the measure of a tangent-chord angle is half the measure of the intercepted arc inside the angle.