Brain Buster 1. Draw 4 concentric circles 2. Draw an internally tangent line to two circles 3. Name two different types of segments that are equal. 4. Explain the difference between a secant & a chord 5. What do you know about a tangent line and the radius drawn to the point of tangency?

Arcs and Section 10.2 Chords

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

Semicircle: An Arc that equals 180° To name: use 3 letters E D EDF P F

THINGS TO KNOW AND REMEMBER ALWAYS A circle has 360 degrees A semicircle has 180 degrees Vertical Angles are Equal

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

Arc Addition Postulate B m ABC = + m BC m AB

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

CONGRUENT ARCS Congruent Arcs have the same measure and MUST come from the same circle or of congruent circles. C B D 45 45 110 A

In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. B C AB  CD IFF AB  DC A D

60 120 120 x x = 60

2x x + 40 2x = x + 40 x = 40

*YOU WILL BE USING THE PYTHAGOREAN THM. WITH THESE PROBLEMS sometimes* If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc. IF: AD  BD and AR  BR THEN: CD  AB C P A R D B *YOU WILL BE USING THE PYTHAGOREAN THM. WITH THESE PROBLEMS sometimes*

What can you tell me about segment AC if you know it is the perpendicular bisectors of segments DB? It’s the DIAMETER!!! A C B

Ex. 1 If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc. x = 24 24 y 60 y = 30 x

Example 2 EX 2: IN P, if PM  AT, PT = 10, and PM = 8, find AT. P A M MT = 6 T AT = 12

RZ = 8 Example 3 In R, XY = 30, RX = 17, and RZ  XY. Find RZ. X R Z

x = 1.5 Example 4 IN Q, KL  LZ. IF CK = 2X + 3 and CZ = 4x, find x.

In the same circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center. B AD  BC IFF LP  PM A M P L C D

Ex. 5: In A, PR = 2x + 5 and QR = 3x –27. Find x.