Question

a circle has a center at 8,2 the point 3, 7 is on the circle, what is the area of the circle to the nearest tenth

Answer 1

We have to calculate the radius
Radius: Distance between the points (8,2) and (3,7)

Given two points (x₁,y₁) and (x₂,y₂) the distance between these points will be:
Distance=√((x₂-x₁)²+(y₂-y₁)²)

In this case:
Distance=radius=√((3-8)²+(7-2)²)=√(25+25)=√50

Area of a circle=πr²
Data:
r=√50

Therefore:
Area of this circle=π((√50)  u)²=50π u²≈157.1 u².

Answer: the area would be:    50π u²      or        157.08 u²