(6) Constructing a straight line parallel to a given straight line (d) and passing through a given point A
Construct AH such that AH is perpendicular to (d). Construct a straight line (e) that passes through A and is perpendicular to the straight line AH , (e) is the straight line passing through A and (e) // (d)
(7) Constructing the circumscribed circle (or circumcircle) of triangle ABC
Draw the perpendicular bisectors of BC and AC , the two lines intersect at O. The circle of center O and radius OA will pass through the points A, B and C (in other words, the circle of centre O, radius OA is the circumcircle of ΔABC).
(8) Construction incircle (or inscribed circle) of triangle ΔABC
Draw the bisectors of angle BAC and angle ABC . This two lines intersect at I. Draw the straight line IJ such that IJ ⊥ BC ( point J is on BC). The circle of centre I, radius IJ is the incircle of triangle ΔABC (the circle contained in the triangle and tangent to the three sides)
(9) Constructing a straight line (d) passing through point A of a given line segment AB and forming with AB an angle which is equal with a given angle xOy.
Draw a circle of center O, radius r cutting the sides Ox, Oy respectively in P and Q. Draw a circle of center A, radius r, cutting AB at point R (AR = OP = OQ = r). Draw a circle of centre R and radius PQ which cuts the circle of centre A at point S. The straight line AS is the line we need to construct.
(10) Constructing a parallelogram ABCD with a given side BC, length AB = a and ∠ABC is equal to a given ∠xOy
Solution: Draw the straight line passing through B and forming with side BC an angle that is equal to angle xOy. This line cuts the circle of center B, radius a at point A. Draw the circle of center A, radius r = BC and the circle of center C and radius a, two circles intersect at point D (as opposed to point B). ABCD is a parallelogram we need to construct.
27.1.2014
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