Problem 5
Each two tangents form a right angle from the center of the circle to the circumference (a radius) and from the circumference to the exterior point. That makes a kite of 2 tangents and 2 radii.
The radii make an angle of 360 - 2*90 - 47 = 133.
That is also the central angle for the arc you are asking about.
Answer: 133.
Problem 9
The center is at point (-6, - 8) So far what you have is
(x + 6)^2 + (y + 8)^2 = r^2
You use the two given points to find r^2
r^2 = (x2 - x1)^2 + (y2 - y1)^2
r^2 = (-6 - 0)^2 + (- 8 - 0)^2
r^2 = 36 + 64
r^2 = 100
The circles equation is (x + 6)^2 + (y + 8)^2 = 100
Answer D
