Question 1: Calculate the measure of the angle inscribed in a semicircle when the diameter is 10 cm, and the inscribed angle subtends the arc at the circumference.

Answer: 90

Question 2: Construct a semicircle with a radius of 5 cm. Draw an inscribed angle on the arc that is not at the endpoints of the diameter. Verify if the angle measures 90°.

Answer: Constructed angle ≈ 90° (students will draw and verify)

Question 3: If an inscribed angle in a circle measures 45°, what is the measure of the intercepted arc?

Answer: 90

Question 4: Plot a diameter of 8 cm and draw an inscribed angle that is not at the endpoints of this diameter. Measure the angle and confirm if it is 90°.

Answer: Approximately 90°

Question 1: A student claims that all angles inscribed in a circle are 90°. Identify and explain the misconception, providing a correct reasoning based on circle theorems.

Answer: Misconception: Only angles inscribed in a semicircle are 90°. Correct reasoning: An inscribed angle subtending a diameter (semicircle) is 90°, but not all inscribed angles are. Others can be different depending on the arc.

Question 2: A circle has a diameter of 12 cm. An inscribed angle subtends an arc of 180°. What is the measure of this inscribed angle? Explain your answer.

Answer: 90° because the inscribed angle subtending a semicircular arc is always 90°.

Question 3: In a circle, an inscribed angle measures 90°. What can you conclude about the arc it intercepts? Justify your reasoning.

Answer: The intercepted arc is a semicircle (180°), since inscribed angles measuring 90° always intercept a 180° arc.

Question 1: A bridge has a semicircular arch. If the diameter of the arch is 20 meters, what is the measure of the angle formed at the highest point of the arch between two points at the ends? Explain your reasoning.

Answer: 90°, because any inscribed angle in a semicircular arch measures 90°.

Question 2: Design a circular park with a diameter of 30 meters. If a walkway runs along the circumference, and a photographer takes a picture including an inscribed angle on the arc, what is the maximum possible measure of this inscribed angle? Explain your reasoning.

Answer: Maximum inscribed angle is 90°, occurring when the angle is inscribed in a semicircular arc.

Question 1: Prove that an inscribed angle subtending a diameter in a circle is always a right angle, using circle theorems and a labeled diagram.

Answer: Proof involves showing that the angle subtends a semicircular arc, hence measuring 180°, and applying the inscribed angle theorem.

Question 2: A circle has an inscribed angle measuring 70° that intercepts a certain arc. What is the measure of the intercepted arc? Show your working.

Answer: 140°, because the inscribed angle is half the measure of the intercepted arc.

Question 1: A student states: 'Any angle inscribed in a circle that is not in a semicircle is less than 90°.' Is this correct? Explain and correct the misconception if needed.

Answer: Incorrect. Not all inscribed angles outside the semicircle are less than 90°. Some can be greater than 90°, depending on the arc.

Question 2: A diagram shows an inscribed angle of 110° with an intercepting arc of 220°. The student concludes the angle is 110°. Identify the mistake and state the correct angle measure.

Answer: Mistake: The angle should be half the arc measure, so 110°, which is correct, but if the student thought it was different, they might have misapplied the theorem.