What Is There To Know About A Circle?Jaime LewisChrystal SanchezAndrew Alas

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• Chord Product theorem –If two chords intersect in the interior of a circle, then the products of the lengths of the segmants of the chords are equal.

A Line Segment Where Both Endpoints On The Circle.

Chords

The red lines representchords in a circle.

• -If two secants intersect in the exterior of a circle, then the product of the lengths of one secant segment and its external segment equals the product if the lengths of other secant segment and its external segment.

• -If a secant and a tanget intersect in the exterior of a circle, then the product of the lengths of the lengths of the secant segment and its external segment equals the length of the tanget segment squared. (WHOLE x OUTSIDE = tanget squared) AE x BE = CE x DE

• -If two secants or chords intersect in the interior of a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

• If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then, there are two useful theorems/formula that allow relate the side lengths of the two given segments

A Line That Intersects Two Points Of A Curve.Secant

The red line representsthe Secant of a circle.

• Point of Tangency: The point where a line intersects a circle.

A Tangent Touches A Circle At One Point And Forms A Right Angle With The Radius.

Tangent

The red line representsa tangent of a circle.

Point of Tangency

• Inscribed Angle- An inscribed angle is an angle formed by two chords in a circle, which have a common endpoint.

An Angle Whose Vertex Is The Center Of The Circle.Central Angle

Central AngleInscribed Angle Theorem

• Minor Arc: Shortest/Smallest Arc.• Major Arc: Longest/Biggest Arc.• Arc Addition Postulate: The measure of an Arc formed by two adjacent Arcs is the sum of the measures of the two Arcs.

• Arc Length= 2πr × X/360• Intercepted Arc- That part of a circle that lies between two lines that intersect it.

A Segment Of The Circumference Of A Circle.Arc

Arc of a circle. The red Arc represents the

Minor and the white Arc the Major Arc.

• An angle subtends a semi-circle when it is a right angle.

An angle between two lines inside the circle if we extend those lines till they meet the circle then take a chord joining them to form a triangle.

Subtends

• An inscribed quadrilateral is any four-sided figure whose vertices all lie on a circle.

Inscribed Quadrilateral in a Circle

• - Area of Sectors of a Circle: A=n/360πr2 or A=CS/πr2.

• - A=n/360πr2 where n is the number of degrees in the central angle of the sector.

• - A=CS/πr2 where CS is the Arc Length of the sector.

Portion Of A Circle Enclosed By Two Radii And An Arc.

Sectors/Sections

Both portions of the circle are sectors.

Area of a Sector of A Circle Formula

• -If a Radius is perpendicular to a Chord, then it BISECTS the Chord.

• -In a Circle, the perpendicular bisector of a Chord is diameter/radius.

Miscellaneous TheoremsTheorems

THAT’S IT FOLKS!