Cynthia is constructing a circle inscribed in a triangle. She has partially completed the construction as shown below. What shou
ld be her next step in the construction?
Select one:
a. Connect vertex B to the arc markings to complete the angle bisector
b. Use a straightedge to find the angle bisectors for angles A and B
c. Connect three arc markings together to form the triangle
d. Use the arc markings to determine the radius to construct the circle
Select one:
a. Connect vertex B to the arc markings to complete the angle bisector
b. Use a straightedge to find the angle bisectors for angles A and B
c. Connect three arc markings together to form the triangle
d. Use the arc markings to determine the radius to construct the circle
2 answers:
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Answer:
Step-by-step explanation:
Consider a sketch of the problem as shown in the picture, where:
- Blue line is given by y = 4x + 1.
- Point B is the center of the circle.
- Point A is (-3, 0).
Since the center of the circle lies on the line y = 4x +1 and is tangent to the x-axis at point A, then its radius BA is perpendicular to the x-axis. To find the coordinates of point B, we must replace x = -3 into the blue line equation: y = 4x(-3) + 1 = -11.
So, we know that the center of the circle is at B=(-3, -11). And furthermore, the radius BA is of length r=11.
Since the <em>general equation of the circle</em> of radius lenght r centered at (h, k) is given by
then with h = -3, k = -11 and r= 11, the equation of our circle is
