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Mathematics Dictionary
Dr. K. G. Shih
Junior High Mathematics
Study Tips and Home Works
How to do the home work ?
  • 1. Answr the questions first in each home work.
  • 2. Then read the related keywords of the given title in JM.
  • 3. Do the questions again as home work.
  • 4. How to back to JM ? Click the Back in 3rd line of this page.


  • J01 | - Study five centers of triangles.
  • J02 | - Study circle and its tangents
  • J03 | - Study factors of numbers
  • J04 | - Geometry : Change quadrilateral to eqaul area triangle
  • J05 | - Binomial expansion by Pascal triangle
  • J06 | - Angle : Various names
  • J07 | - Compare the rhombus and square
  • J08 | - Ortho-center theory
  • J09 | - Circum-center of triangle
  • J10 | - In-center of triangle
  • J11 | - Triangle : Construct a triangle using 3 given lines
  • J12 | - Bisect an angle
  • J13 | - Find the day of week
  • J14 | - There are 100 chicken and rabits together. The feet are 300
  • J15 | - Construct triangle ABC : Given sides AB, AC and median AD
  • J16 | - Construct triangle ABC : Given sides AB, AC and median AD
  • J17 | - Three circles touch each other with same common tangent
  • J18 | - Circle inscribed an equilateral triangle
  • J19 | - Circle inscribed an equilateral triangle
    • Home Works


    J01. Home Work 1 : Study five centers of triangles

    Questions
    • 1. What is the definition of incenter of a triangle ?
    • 2. State how to construct the incenter ?
    • 3. Why the incenter has same distance from the sides of the triangle ?
    • 4. How to draw an incircle ?
    • 5. Draw the escenter of a triangle.
    • 6. Draw ex-cneter E, gravity center G, orthocenter O in a large triangle. Prove that E, G, O are colinear (On same straight line)
    Reference
    Go to Begin

    J02. Home Work 2 : Study circle and it tangents

    Questions
    • 1. What is the definition of a tangent to a circle.
    • 2. How to draw a tangent at point P which is on the circle ?
    • 3. How to draw two tangents from point P to circle when P is outside the circle.
    • 4. Two fixed points A and B.
      • A point P keep same distance from A and B.
      • What is the locus of P ?
    • 5. Two fixed points A and B.
      • A point P moves with AB^2 = PA^2 + PB^2.
      • What is the locus of point P.
    Reference
    Go to Begin

    J03. Home Work 3 : Study factors of numbers

    Questions
    • 1. What is amicable pairs ?
    • 2. Prove that numbers 220 and 284 are amicable pairs.
    • 3. Prove that number 30 is an abundunt number.
    • 4. What is a perfect number ?
    • 5. Find the first 3 perfect number with proof.
    Reference
    Go to Begin

    J04. Home Work 4 : Diagram construction geometry

    Questions
    • Change a quadrilateral to a triangle with same area.
    • Change a pentagon to a triangle with same area.
    Reference
    Go to Begin

    J05. Home Work 5 : Binomial expansion by Pascal triangle

    Questions
    • 1. What is Pascal triangle ?
    • 2. Expand (x+1)^2.
    • 3. Expand (x+1)^3.
    • 4. Expand (x+1)^4.
    • 5. Expand (x+1)^5.
    References
    Go to Begin

    J06. Angle : various names

    Questions
    • Give the names of various angles
    • What is the unit of an angle ?
    • One degree = how many radians ?
    References
    Go to Begin

    J07. Compare the rhombus and the square

    Questions
    • Study subjects : Quadrilaterals and parallelogram
    • Properties of square : Program 06 02
    • Properties of rhombus : Program 06 05
    • Other diagrams : Parallelogram, Rectangle
    Questions
    • Properties of square : Program 06 02
    • Properties of rhombus : Program 06 05
    • Other diagrams : Parallelogram, Rectangle etc.
    References
    Go to Begin

    J08. Ortho-center theory

    Questions
    • Prove by construction that the heights of triangle ABC are concurrent
    • Prove by construction that AO : UR = 2 : 1
      • O is ortho-center and AOF perpendicular to AB
      • U is the circum-center and UR perpendicular to AB
    References
    Go to Begin

    J09. Circum-center of triangle
    Questions
    • 1. What is circum-center
    • 2. Draw a triangle
    • 3. Draw a circle passing the vertices of the triangle
    References
    Go to Begin

    J10. In-center of triangle

    Questions
    • 1. What is in-center of triangle ?
    • 2. Draw a triangle
    • 3. Draw a circle which is inscribed the triangle (Sides tangent to circle)
    References
    Go to Begin

    J11. Construct a triangle using 3 given sides

    Questions
    • Given 3 lines ?
    • Draw a triangle
    References
    Go to Begin

    J12. Bisect an angle

    Questions
    • How to bisect angle ?
    References
    Go to Begin

    J13. Find day of week

    • Q1. What is leap year ?
    • Q2. What is the week day of July 7 of 1937 ?
    Solution
    Go to Begin

    J14. There are 100 chicken and rabits together. The feet are 300

    Question
    • How many rabits ? How many chicken ?
    Method 1 : Assume that there are 100 chicken
    • 1. The feet should be 200
    • 2. The feet exceed 300 - 200 = 100
    • 3. Hence there are 100/2 = 50 rabits
    Method 2 : Assume that there are 100 rabits
    • 1. The feet should be 400
    • 2. The feet not enough 400 - 300 = 100
    • 3. Hence there are 100/2 = 50 chicken
    Verify
    • 50 chicken and 50 rabits
    • Total heads = 100
    • Total feet = 2*50 + 4*50 = 300

    Go to Begin

    J15. Construct triangle : Given sides AB, AC and median AD

    Solution
    Go to Begin

    J16. Construct triangle : Given side AB, medians AD and BE Solution
    Go to Begin

    J17. Three circles touch each other with same common tangent

    Question
    • Circle A toucn circle B with external common tangen RT
    • Circle C touch circle A and circle B and tangent to RT
    • Express radius of circle C in terms of radius of circle A and circle B
    Solution
    Go to Begin

    J18. Circle inscribed an equilateral triangle

    Question
    • Circle touches three sides of an equilateral triangle
    • 2nd circle touches circle and sides AB and AC
    • 3rd circle touches 2nd circle and sides AB and AC
    • If each side is 10 cm, find the radius of the 3rd circle
    Solution
    Go to Begin

    J19. Circle inscribed an equilateral triangle

    Question
    • Circle touches three sides of an equilateral triangle
    • One circle touches circle and sides AB and AC
    • One circle touches circle and sides BC and BA
    • One circle touches circle and sides CA and CB
    • If each side is 10 cm, find the total area of 3 small circles
    Solution
    Go to Begin

    J20.


    Go to Begin
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