Question

In the diagram, ∠ABC = 90°. What is the radius of the circle?


A. 5.7 in
B. 16.5 in
C. 24.6 in
D. 12.3 in

Answer 1

I had that question on my test. its D. 12.3

Answer 2

Answer;

D. 12.3 in

Explanation and solution;

• We are give that ∠ABC = 90°; therefore a line from point A to point C is the diameter, this is because a diameter subtends an right angle to the circumference of the circle.

• Therefore; triangle ABC is a right-angled triangle, thus AC is the hypotenuse.

Using the Pythagoras theorem;

AC² = AB² + BC²

        = 22.1² + 10.9²

        = 607.22

AC = √ 607.22

    = 24.64

But, since AC is the diameter and the radius is half of the diameter, then

Radius = 24.64/2

           = 12.32

           ≈ 12.3  (to 1 decimal place)