In circle O, diameter AOB is drawn and point C is located on the circle such that CA=12 and CB=16. What is the length of the radius of circle O?

radius = 10

Step-by-step explanation:

As AB is the diameter of the circle, the angle ACB inscribes an arc of 180 degrees, so it is a 90 degrees angle, then the triangle ACB is a right triangle, with hypotenusa AB.

We can find the length of the diameter AB using the Pythagoras' theorem:

AB^2 = CA^2 + CB^2

AB^2 = 12^2 + 16^2 = 400

AB = 20

The radius of the circle is half the diameter, so the radius is 20 / 2 = 10

5+2x=a

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