Geometry

Question Analysis

The main focus is to determine whether the point  lies on circle . We need to find the center and radius of circle  using the endpoints of the diameter  and , and then check if the distance from the center to point  is equal to the radius.

 

Key Concept Explanation

1. Center of a circle: The center of a circle with diameter endpoints  and  is the mid - point, calculated by the formula .

2. Radius of a circle: The radius  is the distance from the center  of the circle to any point  on the circle. The distance formula is . If the distance from the center to a point is equal to the radius, then the point lies on the circle.

 

Step - by - Step Solution

1. Find the center of circle :

Given  and , the center  of the circle (mid - point of