Tricks and Traps: Squares Inscribed in Circles
If you see a square inscribed in a circle on the SAT, the test makers are assessing your knowledge of 45:45:90 triangles.
What? Huh? The question is about squares and circles, not triangles! Listen closely, my SAT cohorts: Hidden triangles are often the key to solving the most difficult geometry questions.
Let’s look at an example of an inscribed square problem:
Begin by labeling the diagram with the information provided in the question. Notice that the diameter of the circle is also the diagonal of the square:
If you can find the length of the diagonal, you can find the diameter and radius. Use your knowledge of triangles to find this information:
The two triangles are 45:45:90 triangles, so the hypotenuse is the length of the side multiplied by the square root of 2. The radius is one-half of the diameter:
Now that you know the radius of the circle, you can solve for the area:
The correct answer is (C).
Always be on the lookout for hidden triangles on SAT geometry questions. If you graced with a questions that has a square inscribed in a circle, know that the diagonal of the square, found using 45:45:90 triangle properties, leads to the discovery of the radius.
PowerScore Practice Prep
Can you solve the following math questions? The solutions are listed below.
- A square is inscribed in a circle. The area of the circle is 50π. What is the perimeter of the square?
- A square is inscribed in a circle. If the area of the square is 36, what is the circumference of the circle?
- A square is inscribed in a circle. If the diameter of the circle is 4, what is the area of the square?
What are some of your favorite SAT Math tricks and techniques? Tell us in the comments!