Question

If AB = 5 and AO = 8. What is the length of the radius (r)?AB is tangent to circle O at B. Diagram not drawn to scale.

Answer 1

6.24 units

Step-by-step explanation:

Recall that the angle between a tangent AB and the radius, BO is always 90 degrees.

Therefore, triangle ABO is a right triangle.

Applying the Pythagorean Theorem:

`\begin{gathered} AO^2=AB^2+BO^2 \\ \implies8^2=5^2+r^2 \end{gathered}`

We solve the equation above for r:

`\begin{gathered} r^2=8^2-5^2 \\ r^2=64-25 \\ r^2=39 \\ r=\sqrt[]{39} \\ r\approx6.24 \end{gathered}`

The length of the radius is approximately 6.24 units.