Counter
Mathematics Dictionary
Dr. K. G. Shih

Figures


  • GE 21 01 | - F101 : Sides AB, AC and Median AD are given
  • GE 21 02 | - F102 : Medians AD, AE and side AB are given
  • GE 21 03 | - F103 : Three circles touch each other with same common tangent
  • GE 21 04 | - F104 : Square side a and Four sim-circle radius a/2
  • GE 21 05 | - F105 : Circle inscribed an equilateral triangle (1)
  • GE 21 06 | - F106 : Circle inscribed an equilateral triangle (2)
  • GE 21 07 | - F107 : Square and equaliteral triangle
  • GE 21 08 | - F108 : Area of triangle formed by medians of triangle ABC
  • GE 21 09 | - F109 : Heights and medians of equilateral triangle ABC
  • GE 21 10 | - F110 : Pedal triangle of equilateral triangle
  • GE 21 11 | - F111 : Excentral triangle of equilateral triangle
  • GE 21 12 | - F112 : Pedal triangle of triangle ABC
  • GE 21 13 | - F113 : Ex-central triangle of triangle ABC
  • GE 21 14 | - F114 : Construct 4 congruent triangles using triangle ABC
  • GE 21 15 | - F115 : Ortho-center, centroid and circum-center are colinear
  • GE 21 16 | - F116 : Prove cos(A - B) = cos(A)*cos(B) + sin(A)*sin(B)
  • GE 21 17 | - F117 : Divide equilateral triangle side into 3 eqal parts
  • GE 21 18 | - F118 : Point inside equilaleral triangle to sides equal height
  • GE 21 19 | - F119 : A(7,4), B(3,1), C(0,k) find k if AC + BC is minimum
  • GE 21 20 | - F120 : Hexagon inscribed equilateral triangle
  • GE 21 21 | - F121 : Heights of triangle are concurrent
  • GE 21 22 | - F122 : Bisector of a line
  • GE 21 23 | - F123 : Bisector of an angle
  • GE 21 24 | - F124 : Conditions of two lines in parallel
  • GE 21 25 | - F125 : Angles in a circle
  • GE 21 26 | - F126 : Trinagle sides s = (a + b + c)/2
  • GE 21 27 | - F127 : Circum-center
  • GE 21 28 | - F128 : In-center
  • GE 21 29 | - F129 : Ex-center
  • GE 21 30 | - F130 : Centroid
  • GE 21 31 | - F131 : Ortho-center
  • GE 21 32 | - F132 : Pedal Triangle
  • GE 21 33 | - F133 : Ex-central triangle
  • GE 21 34 | - F134 : Three point define a circle
  • GE 21 35 | - F135 : Tangent to circle (1)
  • GE 21 36 | - F136 : Tangent to circle (2)
  • GE 21 37 | - F137 : Concyclic
  • GE 21 38 | - F138 : How many chords
  • GE 21 39 | - F139 : Centroid
  • GE 21 40 | - F140 : Locus - Examples

  • Answers


    Figure 101 : Sides AB, AC and Median AD are given

    Method : Construct triangle ABC

    Go to Begin

    Q02. Figure 102 : Medians AD, AE and side AB are given

    Method : Construct triangle ABC

    Go to Begin

    Figure 103 : Three circles touch each other with same common tangent

    Method : Find area of small circle

    Go to Begin

    Figure 104 : Square side a and Four sim-circle radius a/2

    Question : Find area of shaded portion

    Go to Begin

    Figure 105 : Circle inscribed an equilateral triangle (1)

    Question : Find area of the smaller circle

    Go to Begin

    Figure 106 : Circle inscribed an equilateral triangle (2)

    Diagram
    Question : Find area of the smaller circles

    Go to Begin

    Figure 107 : Square and equaliteral triangle

    Diagram
    Question

    Go to Begin

    Figure 108 : Area of triangle formed by medians of triangle ABC

    Diagram
    Question
    Note
    • We should remeber the 1/3 rule
    • This diagram is also used to prove that medians are concurrent

    Go to Begin

    Figure 109 : Heights and medians of equilateal triangle ABC

    Diagram
    Heights are concurrent

    Go to Begin

    Figure 110 : Pedal triangle of equilateral triangle ABC

    Diagram
    Construct a pedal triangle

    Go to Begin

    Figure 111 : Ex-central triangle of equilateral triangle

    Construct ex-central triangle

    Go to Begin

    Figure 112 : Pedal triangle of triangle ABC

    Diagram
    Construct Pedal triangle

    Go to Begin

    Figure 113 : Ex-central triangle of triangle ABC

    Diagram
    Construct ex-central triangle

    Go to Begin

    Figure 114 : Construct 4 congruent triangles using triangle ABC

    Diagram
    Reference

    Go to Begin

    Figure 115 : Ortho-center, centroid and circum-center are colinear

    Diagram
    Reference

    Go to Begin

    Figure 116 : cos(A - B) = cos(A)*cos(B) - sin(A)*sin(B)

    Diagram
    Proof

    Go to Begin

    Figure 117 : Divide equilateral triangle side into 3 eqal parts

    Diagram
    Proof

    Go to Begin

    Figure 118 : Point inside equilaleral triangle to sides equal height

    Diagram
    Proof

    Go to Begin

    Figure 119 : A(7,4), B(3,1), C(0,k) find k if AC + BC is minimum

    Diagram
    Proof

    Go to Begin

    Figure 120 : Hexagon inscribed equilateral triangle

    Reference

    Go to Begin

    Figure 121: Heights are concurrent

    Diagram
    Proof

    Go to Begin

    Figure 122 : Bisector of a line

    Diagram
    Method

    Go to Begin

    Figure 123 : Bisector of an angle

    Diagram
    Method

    Go to Begin

    Figure 124 : Conditions of two parallel lines

    Diagram
    Method

    Go to Begin

    Figure 125 : Angles in circle

    Diagram
    Method

    Go to Begin

    F126 : Trinagle sides s = (a + b + c)/2

    Diagram
    Application : See keywords
    • 1. Area of triangle = Sqr(s*(s-1)*(s-b)*(s-c))
    • 2. In-circle : Tangent at A is (s - a)
    • 3. Ex-circle : Tangent at A is s
    • 4. Half angle formula in terms of s

    Go to Begin

    F127 : Circum-center

    Diagram
    Reference
    • GE 02 05
    • GE 03 02

    Go to Begin

    F128 : In-center

    Diagram
    Reference
    • GE 02 06
    • GE 03 02

    Go to Begin

    F129 : Ex-center

    Diagram
    Reference
    • GE 04 08

    Go to Begin

    F130 : Centroid

    Diagram
    Reference
    • GE 02 07
    • GE 03 02

    Go to Begin

    F131 : Ortho-center

    Diagram
    Reference
    • GE 02 08
    • GE 03 02

    Go to Begin

    F132 : Pedal triangle

    Diagram
    Reference
    • GE 03 04
    • See F112

    Go to Begin

    F133 : Ex-central triangle

    Diagram
    Reference
    • See F113

    Go to Begin

    F134 : Three points define a circle

    Diagram
    Reference
    • GE 04 03

    Go to Begin

    F135 : Tangent to circle (1)

    Diagram
    Reference
    • GE 04 02

    Go to Begin

    F136 : Tangent to circle (2)

    Diagram
    Reference
    • GE 04 02

    Go to Begin

    F137 : Concyclic

    Diagram
    Reference

    Go to Begin

    F138 : How many chords ?

    Diagram
    Reference
    • GE 04 05

    Go to Begin

    F139 : Circile inscribed in quadrilateral

    Diagram
    Reference
    • GE 04 06 and GE 04 07

    Go to Begin

    GE 21 40 : Locus - Examples

    Diagram

    Go to Begin

    Show Room of MD2002 Contact Dr. Shih Math Examples Room

    Copyright © Dr. K. G. Shih, Nova Scotia, Canada.

    1