Circle Geometry (Easy)

AMC 10 Q1–8 depth — contest entry, not school drills.

Circle Geometry: core idea

Central angles.

A circle has radius $7$ . Find its diameter.

Hint: Use radius, diameter, arc, and angle relationships. Answer: 14.

1. Find the circumference of a circle with radius $4$ in terms of $\pi$ .
2. A central angle measures $90^\circ$ . What fraction of the circle is its sector?
3. An inscribed angle intercepts a $100^\circ$ arc. Find the angle.
4. Find the arc measure intercepted by a central angle of $72^\circ$ .
5. A radius is perpendicular to a chord. What does it do to the chord? Type $1$ for bisects.
6. Find the circumference of a circle with diameter $12$ in terms of $\pi$ .
7. A semicircle has arc measure how many degrees?
8. A diameter subtends what angle at a point on the circle?
9. Find the radius of a circle with diameter $18$ .