Answer:
2r (1 + √3)
Step-by-step explanation:
Circle O₁ is tangent to AB. Let's call the point of intersection point D. If we draw a radius from the center O₁ to D, we know this forms a right angle.
△ABC is an equilateral triangle, so we know m∠A = 60°. If we draw a line from A to O₁, we know that bisects the angle, so m∠DAO₁ = 30°.
So △DAO₁ is a 30-60-90 triangle. We can find the length AD:
AD = r √3
Now on the other side, circle O₃ is tangent to AB. Let's call the point of intersection point E. We know it's the same triangle we found earlier, so:
EB = r √3
And finally, we can draw a rectangle connecting O₁, O₃, E, and D. The distance between O₁ and O₃ is 2r, so:
DE = 2r.
Therefore:
AB = r√3 + 2r + r√3
AB = 2r√3 + 2r
AB = 2r (1 + √3)
Here's a graph showing the steps. Hopefully this helps, let me know if you have questions!
desmos.com/calculator/hgaonfzxsm
Answer:
center (0;0), vertices (0;10) and (0;-10), foci (0;6) and (0;-6)
Step-by-step explanation:
The answer is 68 hope this helps
Answer:
y=-3/2x+4
Step-by-step explanation:
line is negative, going 3 over 2. y intercept is 4.
Answer:
Perimeter is 38.8 units and approximately 39 units
Step-by-step explanation:
Given: Graph
To find: perimeter of the polygon
Solution:
Distance between points 
is given by 
As per the graph,
point P is (-2,11)
point Q is (-4,6)
point R is (2,0)
point S is (1,7)
point T is (8,7)
Perimeter refers to sum of lengths of all the sides.
Perimeter = 
Or approximately 39 units
