This presentation is the property of its rightful owner.
1 / 11

# What Is There To Know About A Circle? PowerPoint PPT Presentation

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.

What Is There To Know About A Circle?

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

## 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.