Question 431397: Question 4
Part a) Given three noncollinear points, construct the circle and then write the equation of the circle.
The points are A (12,-1), B (6,-3), C (4, 3).
Part b) Using the equation and graph of the circle above, determine if the following lines are tangent, secant or neither.
y=1
y=2x-1
Question 5
Given AC is a diameter of circle O.
AC = 25 cm, measure angle A= 7x+8 and measure angle B = 4x+20. Find the length of arc BC to the nearest tenth.
*Image is not drawn to scale.
Question 6
ABCD is an inscribed quadrilateral. Find the measures of angles A, B, C, D.
*Image is not drawn to scale.
Question 7
Find the area and perimeter of the great circle in the sphere with a radius of 12m.
Question 8
Frederick is paddling due east on the river at 4 mph. However, the river is flowing due north at 2 mph, find the resultant direction and velocity (magnitude) of his canoe
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Question 4
Part a) Given three noncollinear points, construct the circle and then write the equation of the circle.
The points are A (12,-1), B (6,-3), C (4, 3).
Part b) Using the equation and graph of the circle above, determine if the following lines are tangent, secant or neither.
y=1
y=2x-1
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Find the center of the circle by finding the equations of the lines thru the midpoints of AB and BC perpendicular to AB and BC
The intersection of those two bisectors is the center of the circle.
The center is at (8,1)
The radius is the distance from (8,1) to any of the 3 points.
r = 4.5
--> (x-8)^2 + (y-1)^2 = 20.25
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y = 1 goes thru the center
y = 2x-1 does not intersect the circle.
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Reply via the thank you note and I'll send you a graph, and an Excel sheet that gives the equation of a circle defined by 3 points.
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Question 5
Given AC is a diameter of circle O.
AC = 25 cm, measure angle A= 7x+8 and measure angle B = 4x+20. Find the length of arc BC to the nearest tenth.
*Image is not drawn to scale.
Question 6
ABCD is an inscribed quadrilateral. Find the measures of angles A, B, C, D.
*Image is not drawn to scale.
Question 7
Find the area and perimeter of the great circle in the sphere with a radius of 12m.
This is trivial.
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Question 8
Frederick is paddling due east on the river at 4 mph. However, the river is flowing due north at 2 mph, find the resultant direction and velocity (magnitude) of his canoe
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Find the speed using Pythagoras.
v =~ 4.47 mph
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The angle between east and his resultant direction is the arctan(2/4).
angle =~ 26.565 degs north of east
--> 063 degrees (using north as zero and east as 090 degs)
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