Answer:
20 meters
Step-by-step explanation:
Seeing the image attached, we can observe that there is a triangle formed by half of the chord of the arc, the radius (hypotenusa) and part of the radius (r-4). Using pythagoras theorem in this triangle, we have:
(r-4)^2 + 12^2 = r^2
r^2 - 8r + 16 + 144 = r^2
8r = 160
r = 20
So the radius of the circle that contains this arc is 20 meters.
Answer:
20 m
Step-by-step explanation:
radius 'r', half the chord, and dist from center to the chord has formed a right angle triangle
where,
r is hypotenuse
(r-4) = one side i.e dist from center to chord)
12 = other side i.e half the length of the chord)
By applying Pythagoras theorem, we will have
r² = 12² + (r-4)²
r²= 144 + r² - 8r + 16 --->(cancel out r²)
0 = -8r + 160
8r = 160
r = 160/8
r = 20 m
Thus, the radius of the circle containing this arc is 20m
You can also verify this :
distance from center to chord: 20 - 4 = 16
r = [tex]\sqrt{16^{2}+12^{2} }[/tex]
r = 20
