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This problem trains for: SAT-I.

In the circle with diameter AB, AC = 4 units, CB = 3 units. Approximately, what is the shaded area in square units?

figure

figure

Since AB is a diameter, the angle ACB has a measure of 90° and therefore, the triangle ABC is a right triangle.

Since the lengths of the two legs are AC = 4 units, CB = 3 units, they are part of a Pythagorean triple and the hypotenuse must have length AB = 5 units.

However, the hypotenuse is also a diameter and thus the radius of the circle is:

equation

We can obtain the shaded area by subtracting from the area of a semicircle the area of triangle ABC.

The area of the circle is:

equation

The area of the semicircle is:

equation

The area of the right triangle is:

equation

equation