北京 景山 学校 数学系
Advanced Geometry @ MATHEMATICS @ Junior 8/5 。2009-2010
jiguanglaoshi@gmail.com

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[1] October
[updated : 09/10/28]
Date
 Activities / Objectives
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Wednesday

Oct. 21

16:05 -16:45
 • Collect Registration sheets (Ling Lao Shi)

Chapter I

Properties of circles and tangents lines
  • Show on the computer that the locus of the vertex of a right triangle is the circle having the hypothenuse (side opposite to the right angle) as diameter.

  • Show that the tangent is always perpendicular to the radius.

  • Exercise : Show that the line of intersection of two circles is the perpendicular bisector of the intesection.

  • Collect Exercise / Assgnment #1 : constrution of the center of the circumscribed circle.
Locus of vertex of rectangle triangle

 t1

Perpendicular bisector

 ar
 Tangent = limit of secant

 Ta


Construction of the tangent from one point

 T2
Registration Sheet

Assignment #1

Glossary
(Translation of the Geometric words by Ling Lao Shi)
Thursday

Oct. 22

16:05 -16:45
  • Exercises on symmetry of the orthocenter of a triangle with respect of the sides.


  • Solution I (students) : using the inscribed angles properties.


  • Solution II (teacher) : using the properties of the parallelograms.
Sym. of Orthocenter : solution I
orth_Sym1 		Sym. of Orthocenter : solution II
orth_Sym2

Assignment #1 Answers
Wednesday

Oct. 28

16:05 -16:45		 • Return of Assignment #1

• Exercise in class on geometric construction
of the common tangent to two circles :
  • External tangent :
    • Solution I (students) : use the construction of a rectangle.
    • Solution II (teacher) : use the properties of similar triangles.

  • Internal  tangent : use the properties of similar triangles.
Common external tangent (Solution I)
tgt


Common Internal tangent
Tint
 		Assignment #2
 


Common external tangent (Solution II)
tex



Assignment #2




Common Tangent
Answers
Thursday

Oct. 29

16:05 -16:45   
  • Collect Assignment # 2

  • Collect demos in English of the construction of the common tangent to two circles.
  • Handout solutions of Assignment #2 (Euler's problems).
  • Show (computer) anwers of Ass. #2 :
    Have the students practice English reading loud the reasoning in the proposed solutions of the Euler's problems.

  • Hand out Assignment # 3 for Wednesday Nov.4 (morning).
Note : because of Mid-Term exams, classes of Wednesday 11.04  and Thursday 11.05 are CANCELLED
 Euler's line
ED 		Euler's circle
E1

Assignment #2 ANSWERS
(Euler's line & Euler's circle)


Assignment #3
(demos about inscribed angles)