Answer:
5.4
Step-by-step explanation:
At the point of tangency, the degree measure is 90. Hence Angle ABO is 90 degrees. So triangle ABO is right triangle.
In a right triangle, we can use the pythagorean theorem, which says:
Leg1^2 + Leg2^2 = Hypotenuse^2
Where
Leg 1 and Leg 2 are 2 sides of the triangle, respectively, and
hypotenuse is the side "opposite" of the 90 degree angle
In this diagram, thus we can write:
r^2 + AB^2 = AO^2
Now putting the information we know, we can solve for r:
r^2 + 9^2 = (10.5)^2
r^2 + 81 = 110.25
r^2 = 110.25 - 81
r^2 = 29.25
r = Sqrt(29.25)
r = 5.41
Rounded to nearest tenth, it is 5.4, 2nd answer chice is right.
