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Find the coordinates of the center of the circle.
The points on the circle are (22,15), (-25,0), (22,-29).

 Dec 6, 2023
 #1
avatar+259 
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The strategy: We can find the center and radius of a circle by finding the midpoints of two chords, and then the distance between these midpoints. Recall that a midpoint divides a chord into two segments with equal lengths. Therefore, if we know the midpoints of two chords of a circle, then we know the length of each chord, and the distance between these midpoints is equal to the radius of the circle.

 

Step 1: Find the midpoints of two chords. The midpoints of the chords connecting (22,15) and (-25,0), and (22,-29) are (−1.5,7.5) and (-0.5, -14.5), respectively.

 

Step 2: Find the distance between the midpoints. The distance between (−1.5,7.5) and (-0.5, -14.5) is (−1.5−(−0.5))2+(7.5−(−14.5))2​=225​=15.

 

Therefore, the center of the circle is (−1.5,7.5), and the radius is 15.

 Dec 6, 2023
 #2
avatar+33600 
+1

This should help:

 

 Dec 6, 2023

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