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
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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
Go to Begin
F128 : In-center
Diagram
Reference
Go to Begin
F129 : Ex-center
Diagram
Reference
Go to Begin
F130 : Centroid
Diagram
Reference
Go to Begin
F131 : Ortho-center
Diagram
Reference
Go to Begin
F132 : Pedal triangle
Diagram
Reference
Go to Begin
F133 : Ex-central triangle
Diagram
Reference
Go to Begin
F134 : Three points define a circle
Diagram
Reference
Go to Begin
F135 : Tangent to circle (1)
Diagram
Reference
Go to Begin
F136 : Tangent to circle (2)
Diagram
Reference
Go to Begin
F137 : Concyclic
Diagram
Reference
Go to Begin
F138 : How many chords ?
Diagram
Reference
Go to Begin
F139 : Circile inscribed in quadrilateral
Diagram
Reference
Go to Begin
GE 21 40 : Locus - Examples
Diagram
Go to Begin
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