Circle Formulas and Angles Quiz

Circle Area and Perimeter Formulas

• Area of a Circle: Calculated using the formula πr², where r is the radius.
• Circumference of a Circle: The distance around the circle is given by the formula 2πr.

Sector and Segment Formulas

• Area of a Sector: Determined by the formula (central angle/360) * πr².
• Area of a Segment: This represents the area of the sector minus the area of the triangle formed within it, calculated by (central angle/360) * πr² - area of triangle.

Angles Related to Arcs

• Central Angle: The angle formed at the circle's center, equal to the measure of the intercepted arc.
• Inscribed Angle: Formed by two chords and has its vertex on the circle; it measures half of the intercepted arc.
• Angle inside a Circle: Formed by the intersection of two chords, calculated as 1/2 (arc 1 + arc 2).
• Angle outside a Circle: Formed by tangents or secants, calculated as 1/2 (bigger arc - smaller arc).

Segment Lengths and Relationships

• Segment Length Inside Circle: When formed by two intersecting chords, the segments satisfy the relationship (part * part = part * part).
• Segment Length Outside Circle: In secant or tangent relationships outside the circle, the relationship is given by (part outside * whole = part outside * whole).

Tangent and Chord Properties

• Tangent and Radius: A tangent line to a circle is always perpendicular to the radius at the point of contact.
• Chord and Radius Relationship: When a radius bisects a chord, it is perpendicular to that chord.