Circle Theorems-“No Brainers”

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Presentation transcript:

Circle Theorems-“No Brainers” 1. Central Angle Equals the arc 2. Inscribed Angle Equals ½ the arc 3. Diameter ┴ Chord BISECTED chords & arcs Right <‘s formed

(CE)(ED)=(AE)(BE) 4. Angles formed by 2 chords 5. Segments formed by 2 chords POP = POP (CE)(ED)=(AE)(BE) 6. Angle formed by Chord and Tangent Equals ½ the arc

W W 7. Angle formed by 2 secants 8. Segments formed by 2 secants O O WO = WO (whole)(outter) W

Tangent² =(whole)(outter) 9. Angle formed by a tangent & a secant 10. Segments formed by a tangent & a secant T² O T² = WO Tangent² =(whole)(outter) W

right <‘s are formed 11. Radius and Tangent Perpendicular… right <‘s are formed 12. Angle formed by 2 tangents (360-x) x 13. Segments formed by 2 tangents Are equal… ”Clown Hat” Theorem

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 _________. 360º congruent 180º 180º d 2 18. A diameter = ___ radius r 180º

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.