Question

AB is tangent to circle O at B. Find the length of the radius r for AB = 9 and AO = 10.5. Round to the nearest tenth if necessary. The diagram is not to scale.

Answer 1

5.4

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.