The triangle is the simplest geometrical figure having three tops which are in pairs connected among themselves by pieces which form the parties of this polygon. The piece connecting top to the middle of the opposite side is called a median. Knowing lengths of two parties and the median connecting in one of tops it is possible to construct a triangle, without having data on length of the third party or sizes of corners.
Instruction
1. Put the end and designate it by letter A - it will be that top of a triangle in which the median and two parties which lengths (m, an and b, respectively) are known connect.
2. Carry out A piece which length is equal to one of the known parties of a triangle (a) from a point. Designate a point of the termination of this piece by letter B. After that one of the parties (AB) of a required triangle can already be considered constructed.
3. Draw by means of compasses a circle with a radius equal to the doubled median length (2∗m), and with the center in A point.
4. Draw by means of compasses the second circle with a radius equal to length of the second known party (b), and with the center in B point. Postpone compasses for time, but leave on it the measured radius - it is required to you again a little later.
5. Construct the piece connecting A point to a point of intersection of two circles drawn with you. A half of this piece will be a median of a triangle which you build - measure this half and put the end of M. For this moment you have one party of a required triangle (AB) and its median (AM).
6. Draw by means of compasses a circle with a radius equal to length of the second known party (b), and with the center in A point.
7. Carry out a piece which has to begin in B point, pass through a point of M and come to an end in a point of intersection with a straight line with the circle drawn by you on the previous step. Designate a point of intersection by letter C. Now in a required triangle also the unknown under the terms of a task the party of BC is constructed.
8. Connect points of A and C to finish creation of a triangle on two parties of the known length and a median which is carried out from the top formed by these parties.