CIRCLES Everything you wanted to know and then some!!

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Presentation transcript:

CIRCLES Everything you wanted to know and then some!!

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

Secant Line A secant line intersects the circle at exactly TWO points.

TANGENT: a LINE that intersects the circle exactly ONE time

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

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!!

a 2 + b 2 = c 2 x = = x 2

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

A C B

P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters To name: use 3 letters  APB is a Central Angle

measure of an arc = measure of central angle A B C Q 96 m AB m ACB m AE E = = = 96° 264° 84°

Tell me the measure of the following arcs. 80 100 40 140 A B C D R m DAB = m BCA = 240 260

Inscribed Angle: An angle whose vertex is on the circle and whose sides are chords of the circle INSCRIBED ANGLE INTERCEPTED ARC

160  80  To find the measure of an inscribed angle…

120 x What do we call this type of angle? What is the value of x? y What do we call this type of angle?How do we solve for y? The measure of the inscribed angle is HALF the measure of the inscribed arc!!

Examples 3. If m JK = 80 , find m  JMK. M Q K S J 4. If m  MKS = 56 , find m MS. 40  112 

72  If two inscribed angles intercept the same arc, then they are congruent.

Case I: Vertex is ON the circle ANGLE ARC ANGLE ARC

Ex. 2 Find m1. 84 ° 1 m  1 = 42 

Case II: Vertex is inside the circle A B C D ANGLE ARC

Ex. 4 Find m1. A B C D 1 93° 113° m  1 = 103 

Case III: Vertex is outside the circle A B C D ANGLE LARGE ARC small ARC ANGLE LARGE ARC small ARC LARGE ARC ANGLE

A B Ex. 7 Find mAB. 27° 70° mAB = 16 

1 Ex. 8 Find m1. 260° m  1 = 80 

a b c d ab = cd

9 2 6 x x = x x = x x = 1 Ex: 1 Solve for x.

EAB C D EA EB = EC ED

E A B C D x 7 (7 + 13) 4 (4 + x) = Ex: 3 Solve for x. 140 = x 124 = 4x x = 31

E A B C EA 2 = EB EC

E A B C x 24 2 =12 (12 + x) 576 = x x = 36 Ex: 5 Solve for x.