The triangle has an only acute angle
Slope = (y2 - y1)/(x2 - x1) = (1 - 3)/(-2 - (-5)) = -2/(-2 + 5) = -2/3
For perpendicular lines, m2 = -1/m1 = -1/(3/8) = -8/3
A line passing through point (-4, 0) and parallel to the y-axis is x = -4

radius = diameter/2 = 10/2 = 5
center of circle = midpoint of diameter = ((-3 + 5)/2, (1 + 7)/2) = (2/2, 8/2) = (1, 4)
Required equation is (x - 1)^2 + (y - 4)^2 = 5^2
(x - 1)^2 + (y - 4)^2 = 25
Answer:
The answer is three
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The 6 angles with vertex P are:
- Angle APB
- Angle APC
- Angle APD
- Angle BPC
- Angle BPD
- Angle CPD
The letter P must be in the middle since this location is the vertex. Something like angle BPA is the same as angle APB. We can swap the order of the outer letters without any change to the angle itself. Effectively, this means each angle has two possible names.
The number of chairs that still need to be set up are 150.