Question

Angle CCC is inscribed in circle OOO.

\overline{AB}
AB
start overline, A, B, end overline is a diameter of circle OOO.
What is the radius of circle OOO?

Answer 1

5 Units

Explanation:

Khan Academy correct answer

Answer 2

The radius of the circle = 5 units

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