Pr◎per†ies ◎f Circ|es

Kranji Secondary School (Mathematics Department) -- by t๏ђ ฬєє tєςк

Discussion Question 2 (Group 1)



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Can you explain why \(AB \bot OP\) (i.e. \(\angle AQP{\rm{ }} = 90^\circ \))?

Hint : Compare \(\Delta AOQ\) & \(\Delta BOQ\) or \(\Delta APQ\) & \(\Delta BPQ\).



Download the GeoGebra file: http://www.geogebratube.org/material/download/format/file/id/42710
Posted by Toh Wee Teck
Labels: Discussion Question 2 (Group 1)

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Topics

Terms & Definitions

  • Parts of a Circle

Properties of Chords

  • Equal Chords
  • Equidistant Chords
  • Perpendicular Bisector of Chords
  • Midpoint of Chords
  • Perpendicular from Chords

Angle Properties

  • Angles at Circumference & Centre
  • Angles in Semicircles
  • Angles in Same Segments
  • Angles in Opposite Segments
  • [Extra] Angles in Alternate Segments

Properties of Tangents

  • Angles between Tangents & Radii
  • External Points of Circles
Proofs

Properties of Chords (Proof)

  • Equal Chords (Proof)
  • Equidistant Chords (Proof)
  • Perpendicular Bisector of Chords (Proof)
  • Midpoint of Chords (Proof)
  • Perpendicular from Chords (Proof)

Angle Properties (Proof)

  • Angles at Circumference & Centre (Proof)
  • Angles in Semicircles (Proof)
  • Angles in Same Segments (Proof)
  • Angles in Opposite Segments (Proof)
  • [Extra] Angles in Alternate Segments (Proof)

Properties of Tangents (Proof)

  • Angles between Tangents & Radii (Illustration)
  • External Points of Circles (Proof)
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