• Study notes for geometry topics, including circle parts, Pythagorean Theorem, and circle calculations

Circle Parts

• Radius: A segment from the center of the circle to any point on the circle.
• Diameter: A segment that passes through the circle's center with both endpoints on the circle.
• Chord: A segment with both endpoints on the circle.
• Tangent: A line that touches the circle at exactly one point.
• Secant: A line that intersects the circle at two points.
• Arc: A continuous part of the circumference of a circle.
• Central Angle: An angle with its vertex at the center of the circle.
• Inscribed Angle: An angle with its vertex on the circle and its sides as chords.

• Circumference: The total distance around a circle, calculated by 𝐶

  2 𝜋 𝑟 (C = 2πr)

• Area of a Circle: The space inside a circle, calculated by 𝐴

  𝜋 𝑟^2 (A = πr^2)

Pythagorean Theorem

• For a right triangle with legs of 6 cm and 8 cm, the hypotenuse is 10 cm.
• A triangle with sides of 7 cm, 24 cm, and 25 cm is a right triangle.
• The set of side lengths that could not form a right triangle is 7, 10, 12.
• If the diagonal of a rectangle is 13 cm and one side is 5 cm, the other side is 12 cm.
• If a ladder is leaning against a wall with the base 9 feet from the wall and the ladder is 15 feet long, it reaches 12 feet up the wall.

Area and Circumference of Circles

• The circumference of a circle with a radius of 7 cm is 43.96 cm (using 𝜋 ≈ 3.14 ).
• If the area of a circle is 64π square inches, the radius of the circle is 8 inches.
• The circumference of a circular garden with a diameter of 20 feet is 62.8 feet.
• The radius of a circular park with an area of 314 square meters is 10 meters (using 𝜋 ≈ 3.14 ).
• If a bike wheel has a circumference of 78.5 inches, the diameter of the wheel is 25 inches (using 𝜋 ≈ 3.14 ).