Question

What is the length of AB?

Answer 1

R = 14.5

form a right triangle with the 10 as 1st side and r as the hypotenuse.
get the length of the other side using pythagorean.

c = sqrt(14.5^2 - 10^2)  = 10.5

The length from the center to point A = c = 10.5
AB = r - c = 14.5 - 10.5 = 4

length AB = 4

Answer 2

The radius of the circle is given to be r = 14.5

Let the center be O. So OB is the radius = 14.5

We can draw a triangle as shown in the image below. We have a right angled triangle. We know the hypotenuse and the base, we need to find the perpendicular side. This can be done using the Pythagorean theorem.

So, we can write:

$(14.5)^{2}=10^{2}+OA^{2} \\ \\ OA^{2}=110.25 \\ \\ OA=10.5$

Thus, the measure of OA = 10.5

OB = OA + AB

14.5 = 10.5 + AB
⇒
AB = 4