chapter+9+tplesha



definition...

__circle__ - a circle is all points in a plane that are equidistant from a given point in the plane known as the center of the circle.

__radius__ - a segment from the center of the circle to any point on the circle.

__diameter__ - is a chord that contains the center of the circle.

__arc -__ is an unbroken part of a circle, any two distant points.

__semicircle__ - is and arc whose endpoints are endpoints of a diameter. formally called half the circle.

__minor arc__ - of a circle is an arc that is shorter than a semicircle of that circle

__major arc__ - of a circle is an arc that is longer than a semicircle of that circle.

__central angle__ - the angle in a plane of a circle whose vertex is the center of the circle.

__degree measure of arcs__ - the degree measure of a minor arc is the measure of it's central angle. the degree measure of a major arc is 360º minus the degree measure of it's arc. the degree measure of a semicircle is 180º

__Arc Length__ - if r is the radius of a circle and D is the degree measure of an arc of the circle, then the lenth, L, of the arc is given by the following.

find the measures of the arcs AB, BD, and ABD the measure of AB and BD are found from their central angles. mAB =100° mBD= 90° AB and BD, which have just one endpoint in common, are called adjacent arcs. Add their measures to find the measure of ABD mABD =mAB + mBD= 100° + 90° = 190°

chapter 9.2

definitions...

__secant__ - to a circle is a line that intersects the circle at two points.

__Tangent__ - is a line in the plane of the circle that intersects the circle at exactly one point, which is known as the __point of tangency.

Theorem9.2.5__ - The perpendicular bisector of a chord passes through the center of the circle.

__tangent theorem9.2.2__ - if a line is tangent to a circle, then the line is to a radius of the circle drawn to the point of tangency.

__radius and chord theorem9.2.3__ - a radius that is perpendicular to a chord of a circle center of the chord

__converse of the tangent theorem9.2.4__ - if a line is perpendicular to a radius of a circle at it's endpoint on the circle, then the line is perpendicular to the circle

__theorem9.2.5__ - the perpendicular bisector of a chord passes through the center of the circle.

chapter 9.3

definitions...

__inscribed angle__ - is an angle whose vertex lies on a circle and whose sides are chords of the circle.

__Right-Angle Corollary__ - If an inscribed angle intercespts a semicircle, then the angle is a right angle.

__Arc-Intercept Corollary__ - If two inscribed angels intercept the same arc, then they have the same measure

i__nscribed angle theorem9.3.1__ - the measure of an angle inscribed in a circle is equal to the measure of the intercepted arc.

__angle corollary9.3.__2 - if an inscribed angle intercepts a semicircle, then the angle is a right angle.

__arc-intercept corollary9.3.3__ - if two inscribed angle intercept the same arc, the same arc, then they have the same measure.

Find the measure of /_ABC /_ABC is inscribed in circle T and intercepts AC. By angle theorem m /_ABC =½mAC= ½(45º) = 22½º



__[|picture to help you understand]__ chapter 9.4 Theorem - If a tangent and a secant intersect on a circle at the point of tangency, then the measure of the angle formed is 180º or less The measure of it's arc.

Find m /_ ABC in each figure...

A. /_ABC is formed by a secant and a tangent that intersect on the circle. by theorem 9.3.1, m /_ABC =½mAB= ½ (150) = 75 %.

B. /_ABC is formed by two secants that intersect inside the circle. by theorem 9.3.2, m /_ABC =½ (mAC + mBD)= ½ (80% + 40%) = 60%

C. /_ABC is formed by two secants that intersect outside the circle. by theorem 9.3.3, m /_ABC =½ (mAC - mBD)= ½ (80% - 20%) = 30%

__[|picture to help you understand]__

chapter 9.5

theorem9.5.1 - if two segments are tangent to a circle from the same external point, then the segments are equal.

theore9.5.2 - if two intersects outside a circle, the product of the lengths of one secant segment and it's external segment equals the same.

theorem9.5.3 - (whole x outside = tangent squared)

__[|picture to show in real life]__

chapter 9.6

given: x²+y² = 144 sketch a graph when sketching a graph it helps to locate the intercepts. to fin d the x-intercept(s), find the value(s) of x when Y=o

x²+0² = 144 x² = 144 x = ±12 thus, the graph has two x-intercepts, (12,0) and (-12,0) and the y-intercepts are (0,12) and (0,-12)

with this you can locate any point of a circle __[|picture to show points of a circle]__