Skills #2 1. What symbol is used to name circle M? 2. The distance from the center to a point on a circle is __________. 3. The distance across a circle through the center is a ___________. 4. A chord is a segment whose _________ are on the circle. 5. A secant is a line that intersects at circle in _______ points. 6. A tangent is a line that intersects a circle at exactly ________ point(s). 7. The point where a tangent intersects a circle is a _____________. 8. A tangent is ___________ to a radius of the circle. 9. If 2 tangent lines originate at the same external point, the tangents are ______________. 10. A common internal tangent intersects the segment between the ________________ of a circle.
26. Central Angles and Arcs
Central Angles and Arcs Std- MM2G3 – Understand properties of circles Essential Question – How are the angles made by arcs and chords related?
Central angle Central angle- angle whose vertex is the center of a circle A ACB is a central angle C B
Arcs Arc- a piece of a circle. Named with 2 or 3 letters Measured in degrees B ( BP P
Major and minor arcs Minor arc- part of a circle that measures less than 180o (named by 2 letters). Major arc- part of a circle that measures between 180o and 360o. (needs three letters to name) ( AC ( ABC http://www.mathopenref.com/arcminormajor.html
Arc measures Measure of a minor arc- measure of its central angle Measure of a major arc- 360o minus measure of minor arc
Ex: find the arc measures ( m AB= m BC= m AEC= m BCA= 50o ( 130o ( A 180o 180o D ( 180o+130o = 310o 50o 130o C OR 360o- 50o = 310o B
Arc addition The measure of an arc formed by two adjacent arcs is the sum of the measures of those arcs. B A ( ( ( C m ABC = m AB+ m BC
Congruent arcs Congruent arcs- 2 arcs with the same measure MUST be from the same circle OR circles!!!
Example ( m AB=30o A ( m DC=30o E 30o B D ( ( 30o AB @ DC C
Example ( ( ( ( m BD= 45o A m AE= 45o B BD @ AE The arcs are the same measure; so, why aren’t they ? 45o C D E The 2 circles are NOT !