LESSON 11.2 CHORDS AND ARCS OBJECTIVE: To use chords, arcs and central angles to solve problems To recognize properties of lines through the center of a circle
Label each picture as a chord, arc or a central angle: xx arcchord central angle
Theorem 11.4 Within one circle or within (two or more) congruent circles: arcs have central angles central angles have chords chords have arcs (1) (2) (3)
IFS AND THENS
Example #1: In the diagram, circle O circle D. Given that BC PF, what can you conclude? And why (theorem)? O D AND BC PF C B O P D F Theorem: arcs have ’s Theorem: ’s have chords
they are equidistant from the center. they are . center of a circle, then Theorem 11.5 Within one circle or within (2 or more congruent circles): (Biconditional) If chords are equidistant from the (1) (2) If two or more chords are , then
C A B D E F G IF THEN AB CD EG FG IF THEN
Ex. #2 Find a. Give reason (theorem). Therefore, a = So, they are If chords are equidistant from the center of the Circle, then they are . 25 un. THEOREM a and PR are equidistant from center.
Theorem 11.6 In a circle, if a diameter is perpendicular to a chord, then it bisects the chord and its arcs. IF THEN
Theorem 11.7 In a circle, if a diameter bisects a chord (that is not another diameter) then it is perpendicular to the chord. IF THEN
Theorem 11.8 In a circle, if a segment is the perpendicular bisector of a chord, then it contains the center of a circle IF A B THEN AB passes through the center of the circle. A B
Ex. #3 Find r. State the reason (theorem). If KN were extended, it would be a diameter and it is to LM. Therefore, r 2 = r 2 = r 2 = 58 r = 58 If a diameter is to a chord then it bisects the chord. it bisects LM. So, LN = 7. Why?
Ex. #4 Find y. State the reason (theorem) Is this a right triangle? Yes = y = y = y = y If a diameter bisects a chord then it is to the chord. Why?
ASSIGNMENT: Page 593 #1 – 16 Write out the theorem used for #3-16