Find locus of O
Q1. Parallelogram
Question
- Parallelograms keeps the sides unchange
- If A and B are fixed and the parallelogram moves
- The angle C and angle D have bisectors
- The bisectors are intersected at O
- What is the locus of point O ?
Q2. Solution
Solution
- Angle C + angle D = 180 degrees
- Angle OCD + angle ODC = (Angle C + angle D)/2 = 90 degrees
- Hence angle COD = 90 degrees
- Triangle BCE
- Angle BEC = BCE
- Hence BC = BE
- Since BC is fixed length
- Hence E is fixed point
- Triangle ADF
- Angle ADF = AFD
- Hence AF = AD
- Since AD is fixed length
- Hence F is fixed point
- Now points E and F are fixed and angle COD = 90 degree fixed
- Hence point O is a circle with radius EF
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