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# circle

-1
8
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+1406

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
+259
-1

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
+33600
+1

This should help:

Dec 6, 2023