What is the relationship between the angles subtended by the same arc at the cen
Practice Questions
Q1
What is the relationship between the angles subtended by the same arc at the center and at any point on the remaining part of the circle?
They are equal
The angle at the center is double
The angle at the center is half
They are supplementary
Questions & Step-by-Step Solutions
What is the relationship between the angles subtended by the same arc at the center and at any point on the remaining part of the circle?
Step 1: Understand what an arc is. An arc is a part of the circumference of a circle.
Step 2: Identify the center of the circle. This is the point that is equidistant from all points on the circle.
Step 3: Recognize that an angle can be formed by two lines (radii) that meet at the center of the circle.
Step 4: Note that the same arc can create another angle when viewed from any other point on the circle.
Step 5: Measure the angle formed at the center of the circle by the two radii that connect to the endpoints of the arc. This is called the central angle.
Step 6: Measure the angle formed at a point on the circle (not at the center) by the lines connecting that point to the endpoints of the arc. This is called the inscribed angle.
Step 7: Compare the two angles. The central angle is always twice the size of the inscribed angle.
