In this series, we will cover many types of geometric scenarios encountered on the SAT and ACT. A basic knowledge of simple formulas (area, perimeter, etc) is essential, but there are numerous shortcuts to geometry questions that will save you time. Today, we’ll explore circles inscribed squares.
Some things to remember
- The center of the square is the same point as the center of the circle
- Draw lines! Depending on what the question asks for, draw in lines that create simple shapes. (Squares can be turned into triangles, for example).
- Shared angles will normally not be explicitly stated, unless necessary.
- Trust the pictures, but not too much. Inferences must be drawn from fact. Just because it looks like 90-degrees doesn’t mean it is! (Many of these common inferences will be detailed in this series)
- Lengths cannot be negative.
For circles:
- d=2r and all lines from the center to the exterior equal r.
- C = 2πr = πd
- A = πr²
- Tangent lines create right angles with the radius that meets that tangent.
- If you know r, you know everything about the circle!
- Use π = 22/7 with caution. Remember 22/7 > π.
- The diagonal equals (length of a side * √2), since it creates 45-degree angles.
- The intersection of the diagonals creates a right angle.
- When a circle is inscribed inside a square, the side equals the diameter. (Inscribed means that the circle fits perfectly inside the square with its edges touching the side of the square like in the diagram)
Test your SAT math skills with this SAT multiple choice practice question.
