Tdt G Circlegeometrytheorems
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Transcript of Tdt G Circlegeometrytheorems
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Circle geometry theorems
http://topdrawer.aamt.edu.au/Geometric-reasoning/Big-ideas/Circle-
geometry/Angle-and-chord-properties
Theorem Suggested abbreviation Diagram
1. When two circlesintersect, the line
joining their centres bisects their commonchord at right angles.
centres of touchingcircles
2. Equal arcs on circlesof equal radii subtendequal angles at thecentre, andconversely.
equal arcs, equalangles
3. Equal angles at thecentre stand on equalchords, andconversely.
equal chords, equalanglesORangles standing onequal chordsORangles standing onequal arcs
AAMT — TOP DRAWER TEACHERS© 2013 Education Services Australia Ltd, except where indicated otherwise. This document maybe used, reproduced, published, communicated and adapted free of charge for non-commercialeducational purposes provided all acknowledgements associated with the material are retained.
page 1 of 6
http://topdrawer.aamt.edu.au/Geometric-reasoning/Big-ideas/Circle-geometry/Angle-and-chord-propertieshttp://topdrawer.aamt.edu.au/Geometric-reasoning/Big-ideas/Circle-geometry/Angle-and-chord-propertieshttp://topdrawer.aamt.edu.au/http://topdrawer.aamt.edu.au/Geometric-reasoning/Big-ideas/Circle-geometry/Angle-and-chord-properties
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Theorem Suggested abbreviation Diagram
18. The products of theintercepts of twointersecting secants toa circle from anexternal point.
intersecting secants
AP ! BP = CP ! DP
19. Tangents to a circlefrom an external pointare equal.
tangents fromexternal point
20. The angle between atangent and a chord
through the point ofcontact is equal to theangle in the alternatesegment.
angle in alternatesegment
ORangle between tangentand chord
21. The square of thelength of the tangentfrom an external point
is equal to the productof the intercepts of thesecant passingthrough this point.
square of the tangentORintersecting tangent
and secantORtangent and secant
PT 2 = AP ! PB
AAMT — TOP DRAWER TEACHERSpage 5 of 6
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Supplementary theorems
Theorem Suggested abbreviation Diagram
1. Two circles touch if
they have a commontangent at the point ofcontact.
tangent of touching
circles
2. If an interval subtendsequal angles at twopoints on the sameside of it then theendpoints of theinterval and the fourpoints are concyclic.
converse of angles inthe same segment
AAMT — TOP DRAWER TEACHERSpage 6 of 6