1Draw a central angle and an inscribed angle on the same arc on chart paper and cut out the central angle. Fold it into two equal parts and compare with the inscribed angle. What is the conclusion?
2Measure \( \angle AOB \) and \( \angle ACB \) on the same arc AB in three different circles and fill in the table. What is the conclusion?
3How can you show by experimental verification that the angle in a semicircle is a right angle?
4Cut out one of two inscribed angles standing on the same arc and fold it onto the other, or measure both in three circles. What conclusion do you write?
5Prove that the central angle is double the inscribed angle standing on the same arc.
6Prove that an angle in a semicircle is a right angle.
7Prove that inscribed angles standing on the same arc are equal.
8In a circle with centre O, \( \angle AOB = 150^\circ \) and C is on the major arc. Find \( \angle ACB \).
9AB is a diameter and C is on the circle. If \( \angle ABC = 62^\circ \), find \( \angle BAC \).
10When C is on the minor arc, why must you use the reflex angle AOB instead of the ordinary \( \angle AOB \) to find \( \angle ACB \)?
11Inscribed angles on the same arc AB are \( \angle ACB = (2x + 5)^\circ \) and \( \angle ADB = (3x - 20)^\circ \). Find x and the angle.