Solve 9 circle exercises and problems. The exercises and problems cover a range of concepts related to circles, including circumference, area, arc length, sector area, tangent length, inscribed angles, chord properties, segment heights, and Euler's formula for polyhedron inscribed in spheres.
1. Circumference Calculation: Problem: Find the circumference of a circle with a radius of 5 inches.
2. Area Calculation: Problem: Calculate the area of a circle with a diameter of 10 meters.
3. Arc Length Calculation: Problem: Determine the length of an arc with a central angle of 60 degrees in a circle with a radius of 8 centimeters.
4. Sector Area Problem: Problem: Find the area of a sector with a central angle of 45 degrees in a circle with a radius of 12 inches.
5. Tangent Length Problem: Problem: Calculate the length of the tangent from a point 10 feet away from the center of a circle with a radius of 6 feet.
6. Inscribed Angle Problem: Problem: In a circle with a radius of 9 inches, what is the measure of an inscribed angle that intercepts an arc of 60 degrees?
7. Chord Midpoint Problem: Problem: Given a chord of length 10 meters in a circle with a radius of 6 meters, find the distance from the midpoint of the chord to the center of the circle.
8. Segment Height Problem: Problem: Calculate the height of a circle segment with a chord length of 16 inches in a circle with a radius of 10 inches.
9. Euler's Formula Application: Problem: Determine the number of faces of a convex polyhedron inscribed in a sphere with 8 vertices and 12 edges.