Geometry

Question Analysis

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

 

Key Concept Explanation

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

2. Radius of a circle: The radius  is the distance from the center  to any point  on the circle. The distance formula  helps us check if a point lies on the circle. If , 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

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