Presentation on theme: "Circle Theorems-“No Brainers”"— Presentation transcript:
1 Circle Theorems-“No Brainers” 1. Central AngleEquals the arc2. Inscribed AngleEquals ½ the arc3. Diameter ┴ ChordBISECTED chords & arcsRight <‘s formed
2 (CE)(ED)=(AE)(BE) 4. Angles formed by 2 chords 5. Segments formed by 2 chordsPOP = POP(CE)(ED)=(AE)(BE)6. Angle formed by Chord and TangentEquals ½ the arc
3 W W 7. Angle formed by 2 secants 8. Segments formed by 2 secants O O WO = WO(whole)(outter)W
4 Tangent² =(whole)(outter) 9. Angle formed by a tangent & a secant10. Segments formed by a tangent & a secantT²OT² = WOTangent² =(whole)(outter)W
5 right <‘s are formed 11. Radius and TangentPerpendicular…right <‘s are formed12. Angle formed by 2 tangents(360-x)x13. Segments formed by 2 tangentsAre equal…”Clown Hat” Theorem
6 r congruent 360º congruent 180º 180º 2 180º Congruent chords have _____________ arcs.A circle has _________ degrees.Parallel lines intercept _____________ arcs.17. A diameter creates 2 arcs of _________.360ºcongruent180º180ºd218. A diameter = ___ radiusr180º
7 Circle Theorems used in Proofs All diameters or radii of a circle are congruent.Congruent chords intercept congruent arcs.Congruent arcs are intercepted by congruent chords.Parallel chords intercept congruent arcs.A tangent is perpendicular to a radius at the point of tangency.Tangents drawn to a circle from the same exterior point are congruent.Congruent central angles intercept congruent arcs.Congruent arcs are intercepted by congruent central angles.7. Angles inscribed to the SAME arc are congruent.8. Angles inscribed to CONGRUENT arcs are congruent.9. An angle inscribed in a semi-circle is a right angle.10. A triangle inscribed in a semi-circle is a right triangle.Two circles with congruent radii or congruent diameters are congruent.