If the endpoints of the diameter of a circle are (9, 4) and (5, 2), what is the standard form equation of the circle?

The standard forrm equation of the circle is (x-h)² + (y-k)² = r²
where h,k : x,y-coordinate of the center
           r : radius of the circle
Get the center of the circle : h = (x1 + x2)/2 = (9+5)/2 = 7
                                             k = (y1 + y2)/2 = (4+2)/2 = 3
=> the center is (7,3)
Because the given information gave 2 endpoints so we can choose one of these, then use the distance formula to get the radius
                                            r = √(x1 - h)² + (y1 - k)²
                                            r = √(9 - 7)² + (4 - 3)²
                                            r = √2² + 1² 
                                            r = √5
Finally, the equation of the circle is (x - 7)² + (y - 3)² = (√5)²
                                                        (x - 7)² + (y - 3)² = 5

C. 150√3

Step-by-step explanation:

Radius of the inscribed circle is the apothem of the hexagon.

Apothem (a) and half of the side (s) make a 30-60-90 right triangle.

The ratio of the legs, as per property of 30-60-90 triangle:

s : a = 1 : √3 ⇒ s : 5√3 = 1 : √3 ⇒ s = 5

Half the side is s = 5 units, then side of the hexagon is 10 units.

The area of the hexagon:

A = 1/2Pa, P- perimeter, a- apothemA = 1/2(6*10)*(5√3) = 150√3

Correct choice is C