1. Arcs & Angles, Measurement
Circles!
Arcs & Angles, Measurement

2. Arcs & Angles Circle Vocabulary Major Arc: Arc greater than 180⁰.
Minor Arc: Arc less than 180⁰.
Tangent: Line that intersects the circle at 1 point.
Secant: Line that intersects the circle at 2 point.
Chord: Segment whose endpoints are on the circle.
Central Angle: Angle whose vertex is at the center.
Inscribed Angle: Angle whose vertex is on the circle.
DBA DA D AE DB C A DA E
<BCA B
<BDA

3. Arcs & Angles = ? m<1 + m<2 + m<3 = ? mDA + mAB + mBD = ?
Find the Magic Number!
m<1 + m<2 + m<3 = ? D 1
mDA + mAB + mBD = ? C 2 A
Sum of the Angles
= ?
Sum of the Arcs 3 B

4. ½ (big arc – small arc) = angle
Outside Angle C
Use the Magic Number! 1
½ (big arc – small arc) = angle D B D C A E A B A 1 1 B C D

5. Inside Angle Use the Magic Number! ½ (arc + arc) = angle1 C 1 B C A D
½ arc = inscribed angle

6. Angles Both Outside & Inside
Use the Magic Number! D
½ mDBA = m<2 1 C A
½ mDA = m<1 2 E B

7. Right Angles & Circles mDAB = ? 180⁰ m<1 = ? 90⁰ DC is a ? radius.
DE is a ?
tangent. A C
The tangent is perpendicular to the radius. B

8. Right Angles & Circles EACD is a kite! Prove DE ~ EA
Given ED , EA are tangent to C at D, A respectively. 1
If ED , EA are tangent, then <EDC and <EAC are right angles. D
EC ~ EC by the reflexive property.
DC ~ AC because they are radii. A
ΔEDC ~ ΔEAC by HL (hyp-leg). C
DE ~ EA by CPCTC B

9. Angles & Circles Remember <1 & <2 are NOT vertical!
Prove <1 ~ <2
Given DB ~ EA
Remember <1 & <2 are NOT vertical! E D C 2 1 A B

10. Angles & Circles Remember <1 & <2 are NOT vertical!
Prove <1 ~ <2
Given DB ~ EA
Remember <1 & <2 are NOT vertical! E D C 2 1 A B