Circle Geometry

Circumference The entire outside of a circle…duh.

Arcs: Major and Minor A section of the circumference is an arc. The shorter arc AB is the minor arc. The longer arc AB is the major arc. A B

Central vs Inscribed Angles The angle formed by joining the endpoints of an arc to any point on a circle is an inscribed angle. <ACB The angle formed by joining the endpoints of a circle to the centre of a circle is a central angle. <AOB O C B A

Inquiring Minds… _central.htm _central.htm

Central vs Inscribed Angles The inscribed angle is always half the central angle OR the central angle is always double the inscribed angle. 2(<ACB) = <AOB OR <ACB =.5(<AOB ) O C B A

Central vs Inscribed Angles O C B A If <AOB is 80° then what would <ACB be? If <ACB is 35° then what would <AOB be?

Inscribed Angle Properties BT E A I

Inscribed Angle Properties So… <BET = <BAT = <BIT BT E A I

Inscribed Angle Properties So what would angles y° and x° be? What circle properties are we using?

Inscribed Angle Properties Inscribed Angles with the same endpoints are identical… So <ACB = <ADB so angle x° = 55° And a central angle is double the inscribed angle with the same endpoints So <ADB x2 = <AOB so angle y° = 110°

Inscribed Angle Properties #1 Inscribed Angles with the same endpoints are identical, and #2 a central angle is double the inscribed angle with the same endpoints. Remember: The interior angles of a circle total 360°.

Inscribed Angle Properties Where can we start? Solve x°? y°? z° What could we do to start filling in the angles?

50°120° 30° 60° 70° 30° 20° 40° Here’s our angle bank:

Step 1: 2 different Radii Where do we start? What would be step #1?

Step 1: 2 different Radii 18

Step 2: Determine QA 18

Step 2: Determine QA

Step 2: Determine PA

Step 2: Determine PA

Step 1: Determine y

Step 1: Determine y

Assignment Time Pg. 410: 3-6, 11, 12, 15