The coordinates given the circle are not correkt. (Thanks ElectricPavlov!)
1. Determination of the slope of the chords between the points AO and BA.
mAO=yAxA=1−2=−0.5mBA=yB−yaxB−xA=2−1−3−(−2)=−1
2. Determination of the coordinates of the centers of the chords BA and AO.
PBA(xB+xA2,yB+ya2)PBA(−3+(−2)2,2+12)PBA(−2.5,1.5)
PAO(xA+xO2,yA+yO2)PAO(−2+02,1+02)PAO(−1,0.5)
3. Point-direction functions for the center points of the chords BA and AO. The slopes of the function graphs are the negative reciprocals of the slopes of the chords.
fBA(x)=−1mBA(x−xPBA)+yPBAfBA(x)=−1−1(x−(−2.5))+1.5fBA(x)=1(x+2.5)+1.5=x+4fAO(x)=−1mAO(x−xPAO)+yPAOfAO(x)=−1−0,5(x−(−1))+0.5fAO(x)=2(x+1)+0.5=2x+2.5
4. Determine the coordinates of point P by equating the two functions.
x+4=2x+2.5xP=1.5yP=xP+4=1.5+4yP=5.5.P(1.5,5.5)
!