Question

solve this interesting question. don't give meaningless answers​

Answer 1

Answer:

Given three points (1,2),(3,−4)and(5,−6)

Let the coordinates o centre be O(h,k)

The distance from the centre to a point on the circumference is equal to radius.

∴ OA=OB=OC

From distance formula 

OA2=OB2

(h−1)2+(k−2)2=h−3)2+(k+4)2h2−2h+1+k2−4k+4=h2−6h+9+k2+8k+16

−2h−4k+5=−6h+8k+254h−12k=20⟹h−3k=5⟶

(1)OB2=OC2

(h−3)2+(k+4)2=(h−5)2+(k+6)2

h2−6h+9+k2+8k+16=h2−10h++25+k2+12k+36

−6h+8k+25=−10h+12k+61

⟹4h−4k=36⟹h−k=9⟶(2)

=−2k=−4h−3k=5−h±k=−9

∴k=2∴h=11

∴ The Coordinates are (h,k)=(11,2)

Step-by-step explanation:

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