90°: Fluency & Practice
Mathematics
Grade 8
10 questions
~20 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on understanding and applying the fact that the angle in a semicircle is 90°, including procedural practice, reasoning, and real-world problems.
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90°: Fluency & Practice
Subject: MathematicsGrade: Grade 8
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Untitled Worksheet
Grade Grade 8
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
In a circle, a diameter AB is drawn. A point C lies on the circle such that triangle ABC is formed. Calculate the measure of angle ACB.
[2 marks]2.
Construct a triangle where one side is the diameter of a circle and the angle opposite it is a right angle. Mark the right angle clearly.
[3 marks]3.
Prove that any inscribed angle subtended by a diameter is 90°.
[3 marks]4.
A circle has a diameter of 10 cm. If an inscribed angle subtends a point on the circle opposite the diameter, what is the measure of that angle?
[2 marks]5.
Calculate the size of the angle at C in triangle ABC, where AB is the diameter and C is any point on the circle (not at the ends of the diameter).
[2 marks]6.
A chord AC in a circle subtends a right angle at point B on the circumference. If the radius of the circle is 7 cm, and AB = 10 cm, find the length of AC.
[4 marks]7.
In the diagram, AB is the diameter of the circle, and points C and D are on the circle creating angles at the circumference. If angle ACB is 90°, find the measure of angle ADB if D is on the same arc as C.
[2 marks]8.
Explain why an inscribed angle subtended by a diameter always measures 90°, including a brief reasoning.
[3 marks]9.
A semicircular arch has a radius of 15 meters. An arrow hits the lowest point of the arch. What is the angle between the two radii drawn from the center to the points where the arrow hits the arch?
[2 marks]10.
Identify and correct the mistake in the statement: 'Any angle inscribed in a circle that intercepts a diameter is always 45°.'
[3 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet