What is the measure of the angle subtended by a diameter at any point on the cir
Practice Questions
Q1
What is the measure of the angle subtended by a diameter at any point on the circle?
90 degrees
60 degrees
45 degrees
180 degrees
Questions & Step-by-Step Solutions
What is the measure of the angle subtended by a diameter at any point on the circle?
Step 1: Understand what a diameter is. A diameter is a straight line that goes from one side of the circle to the other, passing through the center.
Step 2: Identify what is meant by 'angle subtended by a diameter.' This means the angle formed at any point on the circle when you connect that point to the two ends of the diameter.
Step 3: Recall the inscribed angle theorem. This theorem states that an angle formed by two points on a circle (like the ends of the diameter) and a point on the circle itself is half of the angle at the center of the circle.
Step 4: Since the diameter creates a straight line, the angle at the center is 180 degrees.
Step 5: According to the inscribed angle theorem, the angle at any point on the circle (subtended by the diameter) is half of 180 degrees.
Step 6: Calculate half of 180 degrees, which is 90 degrees.
Step 7: Conclude that the angle subtended by a diameter at any point on the circle is always 90 degrees.
