Geometric Constructions.

This is a forum for construction problems. Rules:

  • As the name says only geometry construction problems are allowed using a straightedge and a collapsible compass only/.
  • A straightedge is an arbitrarily long straight edge, without any markings. You can connect two points, draw a line through a point or draw an arbitrary line using it.
  • A collapsible compass is a circle drawing instrument which cannot be set to specific radii, but can draw a circle centred at a point passing through another, draw a circle centred at a point with an arbitrary radius or draw an arbitrary circle. However, it cannot copy a circle with the same radius after you draw one using it.
  • All constructions must be completely defined. E.g. if you are asked to draw an inscribed rhombus, you must draw any sides that aren't already defined. You cannot leave it as 4 points which satisfy being the vertices of a rhombus.
  • A move is defined as a use of either a straightedge or a collapsible compass. Marking in points doesn't count as a move.
  • A construction can be done in moves if is the minimum number of moves required to create it.
  • When you post solution of \(n-\)th problem you should post \(n+1-\)th problem(with number next to it...),then you get \(3\) points otherwise you'll get \(2\) point and moderator will post next one(problem).
  • If one provides a different construction for any previous problem in the topic (even if it's earlier solved) which uses lesser number of moves then (s)he gets\(3\) more points and \(1\) point of the previous solver is deducted leaving the latter at \(2\).
  • After every problem I will sort the table(so that one with most point's is on top).
  • If the \(n-\)th problem isn't solved for next \(2\) days from the time it was posted then the poster should post new \(n-\) th problem. But if someone solve first (version) of \(n-\)th problem it also counts. And yes must say, exercise your creativity in the limitless space of geometry. ~ XmL

Problem (Easy) 1: In a \(\Delta ABC\), \(T_B \in AC, T_C\in AB\) denotes the feet of the angle bisector corresponding to vertex \(B\) and \(C\), provide a construction as to restore the \(\Delta ABC\) given the vertex \(A\) and the feet of angle bisectors \(T_B, T_C\).

Note by The almighty Knows It All.
2 weeks, 2 days ago

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The almighty knows it all. - 2 weeks, 2 days ago

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