Question

please answer my question ​

Answer 1

Answer:

Circumcentre is at (5,2)

Circumradius is 5

Hope this helps!

Step-by-step explanation:

The circumcentre is at the intersection of the perpendicular bisectors.

The side from (8,6) to (8,-2) is vertical.  Its midpoint is at (8, (6+-2)/2) = (8, 2).  So the perpendicular bisector is the horizontal line through (8,2).  Therefore the circumcentre, which is on this line, has y-coordinate equal to 2.

The side from (8,-2) to (2,-2) is horizontal with midpoint at (5,-2).  The perpendicular bisector is vertical through (5,-2).  Therefore the circumcentre has x-coordinate equal to 5.

Therefore the circumcentre is at (5,2).

The circumradius is the distance from the circumcentre to any of the vertices.  The distance from (5,2) to (8,6) is

√( (8-5)² + (6-2)² ) = √( 3² + 4² ) = √25 = 5.

So the circumradius is 5.