*Notes to a video lecture on http://www.unizor.com*

__Geometry+ 02__

This lecture is dedicated to problems of triangle construction by its certain elements.

The tools of construction are a ruler to draw straight lines and a compass to draw circles.

We will use the following naming rules.

Vertices of triangle will be call by upper case Latin letters

*,*

**A***and*

**B***.*

**C**Sides will be called by lower case Latin letters corresponding to opposite vertices: side

*is opposite to vertex*

**a***etc.*

**A**Angles will be called by lower case Greek letters corresponding to names of their vertices: angle

*is at vertex*

**α***etc.*

**A**Medians are named

*with a subscript of a side onto which they fall: median*

**m***is from vertex*

**m**_{a}*to side*

**A***etc.*

**a**Altitudes are named

*with similar subscripts, like*

**h***etc.*

**h**_{a}Angle bisectors are named

*etc.*

**l**_{a}Radius of a circumscribed circle of a triangle is named

*.*

**R**Radius of an inscribed circle is named

*.*

**r***Problem A*

Construct a triangle by its two sides

*,*

**a***and a median onto its third side*

**b***.*

**m**_{c}*Problem B*

Construct a triangle by its side

*and two medians*

**a***and*

**m**_{a}*.*

**m**_{b}*Hint*: Construct Δ

*where*

**BQR***,*

**BR=a/2***and*

**BQ=2m**_{b}/3*.*

**QR=m**_{a}/3*Problem C*

Construct a triangle by its three medians

*,*

**m**_{a}*and*

**m**_{b}*.*

**m**_{c}*Hint*: Construct Δ

*where*

**PQC***,*

**CQ=2m**_{a}/3*and*

**PQ=2m**_{b}/3*.*

**CP=2m**_{c}/3*Problem D*

Construct a triangle by its side

*and two altitudes onto other sides*

**a***and*

**h**_{b}*.*

**h**_{c}
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