Answer:
The radius of the circle = 5 units
Step-by-step explanation:
Since AB is a diameter of the circle, then CAB is a semi-circle with a total angle measure of 180 degrees.
Now to find the value of the radius of the. circle, we use an important circle geometry principle which states that angle at centre is twice the angle at circumference, this means that angle C is 90 degrees which makes CAB a right triangle with the diameter being the hypotenuse.
Now we can use Pythagoras’ theorem to get the value of the diameter.
Mathematically Pythagoras’ asserted that the square of the value of the hypotenuse equals the square of the value of the opposite added to the square of the value of the adjacent.
Let’s call the hypotenuse h
h^2 = 6^2 + 8^2
h^2 + 36 + 64
h^2 = 100
h = √100
h = 10
But the question asks us to calculate the value of the radius and that is half of the value of the diameter which is 10/2 = 5
