What is the measure of the angle subtended by a diameter of a circle at any poin
Practice Questions
Q1
What is the measure of the angle subtended by a diameter of a circle 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 of a circle 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 'subtended by a diameter.' This means we are looking at the angle formed at a point on the circle when we draw lines from that point to the 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 will always be half of the angle at the center of the circle.
Step 4: Recognize that the angle at the center of the circle formed by the diameter is 180 degrees because it is a straight line.
Step 5: Since the inscribed angle is half of the central angle, the angle subtended by the diameter at any point on the circle is 180 degrees divided by 2, which equals 90 degrees.
Step 6: Conclude that the measure of the angle subtended by a diameter of a circle at any point on the circle is always 90 degrees.
