SHSAT Math · Geometry

Circles Practice

Circumference, area, arcs, and sectors. This is one of the skills tested on the SHSAT; the 2026 exam is computer-based with 50 Math questions in a 90-minute section. Try the samples below, then practice the full topic with instant feedback and explanations.

Free sample questions

Question 1

What is the area of the shaded region if a square with side 8 is inscribed in a circle?

A $8\pi - 16$
B $32\pi - 64$
C $64\pi - 32$
D $16\pi - 32$

Show answer and explanation

Answer: B

Square diagonal =

8\sqrt{2}

= circle diameter, so radius =

4\sqrt{2}

. Circle area =

\pi(4\sqrt{2})^2 = 32\pi

. Shaded area =

32\pi - 64

Question 2

In a circle, a chord of length 16 is 6 units from the center. What is the radius?

Show answer and explanation

Answer: C

The perpendicular from center to chord bisects the chord. Using Pythagorean theorem:

r^2 = 6^2 + 8^2 = 36 + 64 = 100

, so

r = 10

Question 3

A regular hexagon is inscribed in a circle of radius 6. What is the perimeter of the hexagon?

Show answer and explanation

Answer: B

In a regular hexagon inscribed in a circle, each side equals the radius. Side length = 6, perimeter =

6 \times 6 = 36

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Circles Practice

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