Unit 10 Test Study Guide: Circles

Topic 1: Parts of Circles

• Center: Point P in the diagram.
• Radius: Line segment PM.
• Diameter: Line segment NL.
• Chord: Line segment ML.
• Secant: Line segment JL.
• Tangent: Line segment JN.
• Central Angle: Specific angle not labeled, general part of the circle.
• Inscribed Angle: Specific angle not labeled, general part of the circle.
• Minor Arc: NK.
• Major Arc: MLN.
• Semicircle: NKL.

Topic 2: Area and Circumference

• Area and Circumference Calculation
  • Example provided for a circle with unknown radius.
  • Given circumference and area to solve for other circle dimensions.
  • Radius of a circle with circumference 106 cm.
  • Diameter of a circle with an area of 95 square feet.
  • Circumference of a circle with an area of 254 square inches.

Topic 3: Central Angles

• Arc Measurements
  • Calculations required for arc measurements like mEB, mBDE, etc.
• Solve for X
  • Equation given: (6x) and (13x + 3) for angle measures.

Topic 4: Arc Lengths

• Arc Length Calculation
  • For a circle with a radius of 15 cm.
  • Calculate arc lengths for different angles like 1540, 640, 1920, etc.

Topic 5: Chords and Arcs

• Chord and Arc Relationships
  • Given angle measures and relationships to find missing values.
  • Example: mDC (12x + 7), mCB, and mDAB.

Topic 6: Inscribed Angles

• Measure Calculations
  • mML, mLJLK, and solutions for variables when angles are given.
• Tangents
  • If DE and EF are tangent to circle G, find EF.
  • Perimeter finding of a triangle with given side lengths.

Topic 8: Angles and Intersecting Chords, Secants, Tangents

• Angle Measurements
  • Solve for each given angle assuming tangency when segments appear tangent.
  • Examples include mLAED, mLDEC, mZQST.

Topic 9: Segment Lengths

• Calculation of Segment Lengths
  • Solve for X assuming segments that appear tangent are tangent.
  • Multiple examples with different segment configurations and methods to solve for unknowns.

Note: It is important to practice solving problems related to each topic to strengthen understanding and application of circle theorems and properties.