ab is tangent circle O at B find the length of the radius r for ab=10 and ao= 22.3 round to the nearest tenth necessary
Given that AB is tangent to circle O at B, we can draw a right triangle with sides r, r+10, and AO=22.3.
Using the Pythagorean theorem, we have:
(r+10)^2 + r^2 = (22.3)^2
r^2 + 20r + 100 + r^2 = 498.29
2r^2 + 20r - 398.29 = 0
Using the quadratic formula to solve for r, we get:
r = (-20 ± √(20^2 - 4*2*(-398.29)))/2*2
r ≈ (-20 ± √(400 + 3171.16))/4
r ≈ (-20 ± √3571.16)/4
r ≈ (-20 ± 59.8)/4
r ≈ 39.8/4 or r ≈ -79.8/4
r ≈ 9.95 or r ≈ -19.95
Since the radius of a circle cannot be negative, we have r ≈ 9.95.
Therefore, the length of the radius r is approximately 9.95.
wrong
Let's correct the calculation:
We have a right triangle with sides r, r+10, and AO=22.3.
Using the Pythagorean theorem, we have:
(r+10)^2 = r^2 + (22.3)^2
r^2 + 20r + 100 = r^2 + 498.29
20r = 398.29 - 100
20r = 298.29
r = 298.29 / 20
r ≈ 14.9
Therefore, the length of the radius r is approximately 14.9.