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.
6 months, 2 weeks ago

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- 6 months, 2 weeks ago