By using Geometric Construction, you can find the solution of some problems about geometric, such as:

Basic Construction
Construct a line segment congruent to a given line segment; Construct an angle congruent to a given angle; Construct the bisector of an angle; Construct the perpendicular bisector of a line segment; Construct the midpoint of a line segment; Construct a perpendicular to a given line from a given external point; Construct a perpendicular to a given line at a given point on the line; Construct a line through a given external point parallel to a give line; Construct a right angle; Construct a right triangle when the legs are given; Construct a right triangle when a leg and the hypotenuse are given; Construct a right triangle when a leg and the opposite angle are given; Construct a right triangle when a leg and the adjacent acute angle are given; Construct a right triangle when the hypotenuse and an acute angle are given.

Segments
Given line segments a and b. Construct line segment x = a + b; Given line segments a and b. Construct line segment x = a – b; Given a line segment a. Construct line segment x = ma, where m is a natural number. In this example, m = 4; Divide a line segment into n congruent parts. In this example, n = 4; Given a line segment AB = a. Construct line segment x = (m/n)a, where m and n are natural numbers. In this example, x = (3/4)a; Given a line segments a, b and c. Construct a line segment x = ab/c; Divide a line segment internally in ratio a : b; Divide a line segment externally in ratio a : b; Divide a line segment internally in the golden ratio; Divide a line segment externally in the golden ratio.

Angles
Construct an angle congruent to the sum of two given angles; Construct an angle congruent to the difference of two given angles; Given an angle A, A < 90°. Construct a 90°-A angle; Construct a 45°-45°-90° triangle; Construct a 30°-60°-90° triangle; Construct a 18°-72°-90° triangle; Construct a 36°-54°-90° triangle; Construct a 36°-72°-72° triangle.

Circles and Arcs
Construct a circle passing through three noncollinear points; Construct a cricle with a given segment as radius and passing through two given points; Construct the center of a given arc; Construct the midpoint of a given arc; Construct the tagent to a circle through a given point on the circle; Construct the tagents to a circle through a given point not on the circle; Construct the external tangents to two given circles; Construct the internal tangents to two given circles; Upon a given line segment as a chord, construct an arc of a circle in which a given angle can be inscribed; Construct the Apollonius circle.

Triangles
Construct a triangle when three sides are given; Construct a triangle when two sides and the angle opposite one of them are given; Construct a triangle when two sides and the adjacent angle are given; Construct a triangle when a side, an adjacent and the opposite angle are given; Construct a triangle when a side and the two adjacent angles are given; Construct a triangle when ha, ma, la are given.

Polygons
Circumscribe a circle about a given rectangle; Construct a parallelogram when two sides and the angle between them are given; Inscribe a circle in a given rhombus; Inscribe a circle in a given quadrilateral; Inscribe a square in a given triangle.

Regular Polygons
Inscribe an equilateral triangle in a circle; Inscribe a square in a circle; Inscribe a regular pentagon in a circle; Inscribe a regular hexagon in a circle; Inscribe a regular octagon in a circle; Inscribe a regular decagon in a circle; Circumscribe a square about a circle; Construct an equilateral triangle when a side is given; Construct a square when a side is given; Construct a regular pentagon when a side is given; Construct a regular hexagon when a side is given.

Triangle Centers
Incenter (Construct the incenter, inradius and incircle of a triangle; Construct the incentral triangle of a triangle; Construct the A-excenter, A-exradius and A-excircle of a triangle; Construct the excentral triangle of a triangle; Construct the A-incenter-excenter circle of a triangle); Centroid (Construct a median of a triangle; Construct the centroid of a triangle; Construct the medial triangle of a triangle); Circumcenter (Construct the circumcenter, circumradius and circumcircle of a triangle); Orthocenter (Construct an altitude of a given triangle; Construct the orthocenter of a given triangle; Construct the orthic triangle of a given triangle); Nine-point center (Construct the nine-point center and the nine-point circle of a given triangle. Solution 1; Construct the nine-point center and the nine-point circle of a given triangle. Solution 2; Construct the Euler line of a given triangle; Construct the Euler points and the Euler triangle of a given triangle); Symmedian point (Construct a symmedian of a given triangle; Construct the symmedian point of a given triangle); Gergonne point (Construct the Gergonne point of a given triangle; Construct the intouch triangle of a given triangle); Nagel point (Construct the Nagel point of a given triangle); Spieker center (Construct the Spieker center of a given triangle); Feuerbach point (Construct the Feuerbach point of a given triangle; Construct the Feuerbach triangle of a given triangle); Fermat point (Construct the Fermat point of a given triangle).

Transformations
Reflection (Construct the reflection of a point in a line; Construct the reflection of a point in a point); Homothety (Construct the homothetic centers of two circles); Inversion (Construct the inverse image of a point. Case 1. The given point is outside the inverse circle; Construct the inverse image of a point. Case 2. The given point is inside the inverse circle; Construct the inversion pole of a given line; Construct the inverse image of a given line; Construct the inverse image of a given circle).

Extremal Problems
Heron’s Problem

Advanced Problems
Radical center (Construct the radical axis of two circles; Construct the radical center of three circles); Apollonius circles (Construct Apollonius circles no 1 and 2; Construct Apollonius circles no 3 and 4; Construct Apollonius circles no 5 and 6; Construct Apollonius circles no 7 and 8); Soddy circles (Construct the outer Soddy circle; Construct the inner Soddy circle); Malfatti circles (Construct the Malfatti circles); Arbelos (Construct the Archimedean circles; Construct the incircle of an arbelos. Solution 1; Construct the incircle of an arbelos. Solution 2; Construct the incircle of an arbelos. Solution 3).

Euclid’s Elements
Collapsible compass; Construct the center of a given circle.

Articles
Golden Ratio

You can download Geometric Construction from: http://www.dekovsoft.com/gc/gc.exe