Hope it helps with your work
The radius of the circle would be 12
RS is perpendicular to MN and PQ.
We can use the slopes of these lines to determine the answer.
Slope is given by the formula
m=.
Using the coordinates for M and N, we have:
m=.
Since PQ is parallel to MN, its slope will be as well, since parallel lines have the same slope.
Using the coordinates for points T and V in the slope formula, we have
m=.
This is not parallel to MN or PQ, since the slopes are not the same.
We can also say that it is not perpendicular to these lines; perpendicular lines have slopes that are negative reciprocals (they are opposite signs and are flipped). This is not true of TV either.
Using the coordinates for R and S in the slope formula, we have
m=. Comparing this to the slope of RS, it is flipped and the sign is opposite; they are negative reciprocals, so they are perpendicular.
Answer:
Raymond's mistake was on the last step, since he didn't square root both sides
The correct answer should be

Step-by-step explanation:

Good luck!