Geometry

Question Analysis

The main focus is to determine if point  lies on circle Q. We first 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, calculated by .

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

 

Step - by - Step Solution

1. Find the center of circle Q:

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

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