10.3 – Apply Properties of Chords

In the same circle, or in congruent circles, two ___________ arcs are congruent iff their corresponding __________ are congruent. A B C D then minor chords

If one chord is a _________________ _________ of another chord, then the first chord is the _________________. then perpendicular bisector diameter and is the diameter

If a ____________ of a circle is perpendicular to a chord, then the diameter ____________ the chord and its arc. then diameter bisects and the diameter

In the same circle, or in congruent circles, two chords are congruent iff they are _________________ from the _____________. then equidistantcenter and

1. Find the given measure of the arc or chord. Explain your reasoning. =105° Congruent chords

1. Find the given measure of the arc or chord. Explain your reasoning. = Congruent chords = 90°

1. Find the given measure of the arc or chord. Explain your reasoning. = 360 – Congruent chords = 122°

1. Find the given measure of the arc or chord. Explain your reasoning. = Congruent arcs 6

1. Find the given measure of the arc or chord. Explain your reasoning. = Diameter bisects chord 22

1. Find the given measure of the arc or chord. Explain your reasoning. = 119° 61° 119° Diameter bisects arc

=100° 50°

360 – 85 – 65 2 = =105°

Find the value of x. 3x + 16 = 12x = 9x = 9x 1 = x

Find the value of x. 3x – 11 = x + 9 2x – 11 = 9 2x = 20 x = 10

YES or NO Reason: _______________________ it is perpendicular and bisects

YES or NO Reason: _______________________ it doesn’t bisect

10.6 – Find Segment Lengths in Circles

If two chords intersect in the _______________ of a circle, then the ___________ of the lengths of the segments of one chord is equal to the product of the lengths of the segments o f the other chord. interior product

If two secant segments share the same endpoint ____________ a circle, then the ______________ of the lengths of one secant segment and its external segment equals the _____________ of the lengths of the other secant segment and its external segment. outsideproduct

If a secant segment and a tangent segment share an endpoint ____________ a circle, then the product of the lengths of the secant segment and its external segment equals the ___________ of the length of the tangent segment. outside square

Find the value of x. 3  x = 9  5 3x = 45 x = 15

Find the value of x. 3x = 5(5+10) 3x = 75 x = 25

Find the value of x. x 2 = 2(2+16) x 2 = 36 x = 6

Find the value of x. 6  x = 8  3 6x = 24 x = 4

Find the value of x. 2  x = 5  5 2x = 25 x = 12.5

Find the value of x. 5(x + 5) = 6(6+4) 5x + 25 = 60 x = 7 5x = 35

Find the value of x. x 2 = 3(3+24) x 2 = 81 x = 9

Find the value of x. 2x  3x = 3  18 6x 2 = 54 x 2 = 9 x = 3

Find the value of x = 20(x + 20) 961 = 20x = 20x = x

, , 4, 6, 9, 13, 17 HW Problem 10.6 #6 8(x + 8) = 6(10+6) 8x + 64 = 96 x = 4 8x = 32