Question

In circle M, segment AB is tangent to the circle at point C. AB has endpoints such that AM BM  ,


AC  9 and BC  4 . What is the length of the radius of circle M. Show how you arrived at your answer.

Answer 1

Answer:

6

Step-by-step explanation:

We can use the geometric mean theorem:

The altitude on the hypotenuse is the geometric mean of the two segments it creates.

In your triangle, the altitude is the radius CM and the segments are AC and BC.

$CM = \sqrt{AC \times BC} = \sqrt{ 9 \times 4} = \sqrt{36} = \mathbf{6}\\\text{The radius of the circle M is \large \boxed{\mathbf{6}} }$

Answer 2

The length of the radius of the circle is 6 units

How to determine the radius of the circle?

The given parameters are:

AC = 9

BC = 4

To calculate the radius (r), we make use of the following equation:

$r = \sqrt{AC * BC}$

Substitute known values

$r = \sqrt{9 * 4}$

Evaluate the product

$r = \sqrt{36}$

Evaluate the square root

$r = 6$

Hence, the length of the radius of the circle is 6 units

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