Question 1: Calculate the measure of the inscribed angle in a semicircle where the diameter measures 10 cm.

Answer: 90

Question 2: In a circle, an inscribed angle subtends a diameter. What is the measure of this angle?

Answer: 90

Question 3: Construct a semicircle with a diameter of 8 cm. Draw an inscribed angle in the semicircle and measure it.

Answer: 90

Question 4: Explain why any inscribed angle in a semicircle is always 90°, including a brief diagram description.

Answer: An inscribed angle subtends a diameter, which always passes through the center. The angle at the circumference intercepts a semicircle, forming a right angle because of the circle theorem.

Question 5: A circle has a radius of 6 cm. A diameter is drawn, and a point on the circle forms an inscribed angle with the endpoints of the diameter. What is the value of this angle?

Answer: 90

Question 6: Given a triangle inscribed in a circle with one side as the diameter, prove that the angle opposite the diameter is 90°.

Answer: Using the circle theorem, the inscribed angle subtending the diameter is 90°.

Question 7: A chord in a circle subtends a 90° inscribed angle at a point on the circle. If the chord measures 12 cm, what is the radius of the circle?

Answer: 6√2 cm

Question 8: In a real-world scenario, a playground circle has a diameter of 20 m. Find the measure of a shadow cast by a pole placed at a point on the circle, considering the angle inscribed in the semicircle.

Answer: 90° (the inscribed angle property applies)

Question 9: Construct a diagram of a circle with a diameter and an inscribed angle. Label all parts and verify the angle measures 90°.

Answer: Inscribed angle equals 90° as per theorem.

Question 10: Identify and correct the mistake in the following statement: 'All angles inscribed in a circle are 90°,' with explanation.

Answer: Incorrect; only angles inscribed in a semicircle are 90°. Other inscribed angles can have different measures.