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### What Is There To Know About A Circle?

Jaime Lewis

Chrystal Sanchez

Andrew Alas

Presentation Theme By PresenterMedia.com

Chords

A Line Segment Where Both Endpoints On The Circle.

- 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.

The red lines represent

chords in a circle.

Secant

A Line That Intersects Two Points Of A Curve.

- -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

The red line represents

the Secant of a circle.

Tangent

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

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

Point of Tangency

The red line represents

a tangent of a circle.

Central Angle

An Angle Whose Vertex Is The Center Of The Circle.

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

Inscribed Angle Theorem

Central Angle

Arc

A Segment Of The Circumference Of A Circle.

- 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.

Arc of a circle. The red Arc represents the Minor and the white Arc the Major Arc.

Subtends

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.

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

Inscribed Quadrilateral in a Circle

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

Sectors/Sections

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

- - Area of Sectors of a Circle: A=n/360πr2 or A=CS/πr2.
- - A=n/360πr2where n is the number of degrees in the central angle of the sector.
- - A=CS/πr2 where CSis the Arc Length of the sector.

Area of a Sector of A Circle Formula

Both portions of the circle are sectors.

Theorems

Miscellaneous Theorems

- -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.

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