Points on a Circle 

       _____
    _I/  X  \__
   /     |     \
  /      M      \
 /       |       \
Y----K---O--------Y'
 \       |       /
  \      N      /
   \_J   |   __/
      \__X'_/
  • Given a circle (c) with center O and diameters X'OX and Y'OY perpendicular to each other.
  • M is the middle of OX.
  • The circle of center M and radius MY cuts OX' at N.
  • The circle of center Y and radius YN cuts (c) at I and J.
  • The perpendicular from M to YN cuts OY at K.
Demonstrate that I, J, K are on the same straight line.

Hint: with this problem, there are two ways of drawing a regular pentagon within a circle.

Source: Reader Philippe Fondanaiche's personal wording from different books on how to draw a regular pentagon within a given circle.

Solution
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