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Geometrical Constructions 1.
Year 2005/06
1 st (fall) semester
1ST DRAWING
Tint-drawing, size A2
Deadline for delivery: Nov.15
Title of a figure is in parenthesis.
1)
Erect a perpendicular to a straight line from a point not lying on the line. (PERPENDICULAR)
2)
Bisect a given angle. (ANGLE BISECTOR)
3)
Construct the angles of 45° and 60°. (ANGLES 45° AND 60° )
4)
Construct the circumscribed circle of a triangle. (CIRCUMSCRIBED CIRCLE)
5)
Construct the inscribed circle of a triangle. (INSCRIBED CIRCLE)
6)
Construct the tangents to a circle from an external point. (TANGENTS OF A CIRCLE)
7)
Construct the tangents to two given circles of different radii. (TANGENTS OF CIRCLES)
8)
Construct the circle tangent to a given line and a given circle at a given point. (TANGENT CIRCLE)
9)
Construct circles with given radius tangent to a pair of intersecting lines. (TANGENT CIRCLES)
10)
Divide a segment into three parts at the ratio of 2:3:5. (DIVISION OF A SEGMENT)
11)
Construct triangle, the lengths of one side and two medians are given. One of the medians is assigned to
the given side. (CONSTRUCTION OF TRIANGLE)
12)
Construct right triangles, the radius of the circumscribed circle and the height assigned to the
hypotenuse are given. (CONSTRUCTION OF RIGHT TRIANGLE)
13)
Construct quadrilateral, the length of a pair of adjacent sides and their angle, another angle and the
angle of diagonals are given. (CONSTRUCTION OF QUADRILATERAL)
14)
Construct trapezium, given one of the two bases, the two angles lying on it and one more side of it are
given. (TRAPEZIUM)
15)
Construct a regular hexagon. Magnify it by 2 from a center of central similarity transformation.
(HOMOTHECY)
16)
Rotate a regular triangle about its center by 45°. (ROTATION)
17)
Apply reverse similarity transformation for a circle with respect to a given point and ratio of – 0.5.
(REVERSE SIMILARITY)
18)
Draw the locus of a point P that is equidistant from two given points. (LOCUS OF POINT)
Oct. 17, 2005, Budapest
dr. Pál Ledneczki
associate professor
T:\tanszek\2005\oktatas_osz\En-GeoC1 \Drawings\drawing1_2005_fall.doc