1. The angle subtended by a segment smaller than a semicircle is — —.
2. The angle subtended by a segment of a circle greater than a semicircle is _____.
3. The angle in a circular segment larger than a semicircle is an obtuse angle.
4. An angle in a segment greater than a semicircle is an obtuse angle.
5. An angle in a segment larger than a semicircle is an obtuse angle.
6. Prove that an angle in a segment greater than a semicircle is an acute angle.
7. The angle in a segment smaller than a semicircle is _____.
8. Prove that an angle subtended by a semicircle is a right angle.
9. An angle in a segment smaller than a semicircle is an ____.
10. Prove with reasoning that an angle in a segment greater than a semicircle is an acute angle.
11. Prove that the central angle subtended by the same arc is twice the inscribed angle.
12. An angle subtended by a larger segment of a circle is an acute angle compared to the angle subtended by a semicircular segment.
13. The measure of an angle subtended by a semicircle is _____.
14. The radius of a circle is 28 cm. What is the radian measure of the central angle subtended by an arc of length 5.5 cm on this circle?
15. The distance between two pillars is 150 meters. One is three times taller than the other. From the midpoint of the line segment connecting the bases of the two pillars, the angles of elevation to the tops of the pillars are complementary. Find the height of the shorter pillar.
16. In a right-angled triangle, the hypotenuse is 6 cm longer than one of the other two sides and 12 cm longer than the other. Find the area of the triangle.
17. If the central angle of a circle centered at point O is 300°, then the angle subtended at the circumference by the same arc will be 60°.
18. Prove that the central angle subtended by an arc of a circle is twice any inscribed angle subtended by the same arc.
19. If the radius of a circle is 7 cm, then what will be the radian measure of the central angle subtended by an arc of length 5.5 cm?
20. Prove that an angle in a semicircle is a right angle.
21. An inscribed angle subtended by the same arc is half of the central angle subtended by that arc.
22. The measure of all inscribed angles subtended by the same arc in a circle is equal.
23. An angle in a segment larger than a semicircle.
(a) Acute angle. (b) Obtuse angle. (c) Right angle. (d) Straight angle.
24. Prove that the central angle subtended by an arc of a circle is twice the inscribed angle subtended by the same arc.
25. Prove that the central angle subtended by an arc of a circle is twice the inscribed angle subtended by the same arc.
26. Prove that the angle subtended by an arc at the center of a circle is twice the angle subtended by the same arc at any point on the circumference.
27. The radius of a circle is 28 cm. Find the radian measure of the central angle subtended by an arc of length 5.5 cm.
28. The radius of a circle is 28 cm. What is the circular measure of the central angle subtended by an arc of length 5.5 cm in that circle?
29. Prove that the central angle subtended by an arc of a circle is twice any inscribed angle subtended by the same arc.
30. The central angle subtended by an arc of a circle is twice the inscribed angle subtended by the same arc—prove it.
