CIRCLE

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MATHEMATICS PROJECT : 2 Made by-: Pritam Kondar Otur,Tal -: Junnar Dist-: Pune

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Chapter 6 Circles

Parts of a Circle:

Parts of a Circle Circle – set of all points _________ from a given point called the _____ of the circle. C Symbol: equidistant center C

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CHORD: a segment whose ________ are on the circle endpoints

Radius:

P RADIUS: distance from the _____ to a point on the circle center Radius

Diameter:

Diameter P DIAMETER: distance ______ the circle through its ______ center across Also known as the longest chord.

What is the relationship between the diameter and the radius of a circle?:

What is the relationship between the diameter and the radius of a circle? r = OR D = ½ D 2 r

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12 32 9 6 D = ? r = ? r = ? D = ? 24 16 4.5 12

Use P to determine whether each statement is true or false.:

Use P to determine whether each statement is true or false . P Q R T S

Secant Line:

Secant Line A secant line intersects the circle at exactly TWO points. SECANT sounds like second

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TANGENT: a LINE that intersects the circle exactly ONE time

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Point of Tangency

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Name the term that best describes the line. Secant Radius Diameter Chord Tangent

Two circles can intersect…:

Two circles can intersect… in two points one point or no points

No points of intersection (different center):

No points of intersection (different center)

No points of intersection (same center):

Concentric Circles No points of intersection (same center) Same center but different radii

1 point of intersection (Tangent Circles):

1 point of intersection (Tangent Circles) Internally Tangent Externally Tangent

2 points of intersection:

2 points of intersection

Common Tangents:

Common Tangents Internal

Common Tangents:

Common Tangents External

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INTERIOR A point is inside a circle if its distance from the center is less than the radius. 

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EXTERIOR A point is outside a circle if its distance from the center is greater than the radius. 

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A point is on a circle if its distance from the center is equal to the radius. 

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If a line (segment or ray) is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. Point of Tangency More Pythagorean Theorem type problems! Yeah!! 

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1. Find x 9 x A B 12 a 2 + b 2 = c 2 x = 15 9 2 + 12 2 = x 2

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2. Find RQ a 2 + b 2 = c 2 8 P R 12 Q RQ = 16 12 2 + (QR) 2 = (8+12) 2 12 2 + (QR) 2 = 20 2

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3. Find the radius. r 2 + 24 2 = (r + 16) 2 16 A B 24 C r = 10 r 2 + 576 = r 2 + 32r + 256 320 = 32r

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R S T If two segments from the same exterior point are tangent to a circle, then they are congruent. Party hat problems!

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R S T 4. Find x

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A C B 5. Find x

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A C E B D 6. Find x. P

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T S Q P N R 7. Find NP

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