# If the points A ( 4 , 3 ) and B ( x , 5 ) are on the circl

Bailee Short 2022-06-25 Answered
If the points $A\left(4,3\right)$ and $B\left(x,5\right)$ are on the circle with center $O\left(2,3\right)$ find the value of x.
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candelo6a
Step 1
AB is a chord.
Midpoint: $M=\left(x/2+2,,4\right)$ .
1) Slope AB:
${m}_{1}:=\frac{5-3}{x-4}=\frac{2}{x-4}$ .
2) Slope MO:
${m}_{2}:=\frac{4-3}{x/2+2-2}=2/x.$ .
${m}_{1}$ is perpendicular to ${m}_{2}$:
${m}_{1}{m}_{2}=-1.$ .
Hence $x/2-2=-x/2;$ ;
$x=2$

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George Bray
Step 1
That would require the line segment AB to be the diameter for M to be equal to O which is not necessarily true.
It is possible that AB doesn't pass through O.

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