# Geometry construction problems - math problems

#### Number of problems found: 54

• Draw a
Draw a triangle ABC, if you know: alpha = 60° side b = 4 cm side a = 10 cm
• Divide an isosceles triangle
How to divide an isosceles triangle into two parts with equal contents perpendicular to the axis of symmetry (into a trapezoid and a triangle)?
• As shown
As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6, then the perimeter of △ BDE
• Vertex points
Given the following points of a triangle: P(-12,6), Q(4,0), R(-8,-6). Graph the triangle. Find the triangle area.
• Construction
Construction the triangle ABC, if you know: the size of the side AC is 6 cm, the size of the angle ACB is 60° and the distance of the center of gravity T from the vertex A is 4 cm. (Sketch, analysis, notation of construction, construction)
• Trapezoid - construction
Construct a trapezoid KLMN, where: k = 9 cm, l = 4 cm, m = 5 cm and angle α = 45°
• Larger perimeter
There are a square and a circle that passes through two adjacent vertices of the square (end points of side a) and the center of the opposite side (c). Which of the plane shape has a larger perimeter?
• Construction of trapezoid
Construct a trapezoid if b = 4cm, c = 7cm, d = 4,5cm, v = 3 cm (Procedure, discussion, sketch, analysis, construction)
• Side lengths
In the triangle ABC, the height to the side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b.
• Outside tangents
Calculate the length of the line segment S1S2 if the circles k1 (S1, 8cm) and k2 (S2,4cm) touch the outside.
• Draw triangle
Construct an isosceles triangle ABC, if AB = 7cm, the size of the angle ABC is 47°, arms | AC | = | BC |. Measure the size of the BC side in mm.
• Construct rhombus
Construct rhombus ABCD if given diagonal length | AC | = 8cm, inscribed circle radius r = 1.5cm
• Parallels and one secant
There are two different parallel lines a, b, and a line c, that intersect the two parallel lines. Draw a circle that touches all lines at the same time.
• Construct
Construct a triangle ABC inscribed circle has a radius r = 2 cm, the angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction and description.
• Two chords
There is a given circle k (center S, radius r). From point A which lies on circle k are starting two chords of length r. What angle does chords make? Draw and measure.
• Intersections
Find the intersections of the function plot with coordinate axes: f (x): y = x + 3/5
• Two heights and a side
Construct triangle ABC when the given side is c = 7 cm, height to side a va = 5 cm and height to side b: vb = 4 cm.
• Triangles
Ivo wants to draw all the triangles whose two sides of which have a length of 4 cm and 9 cm, and the length of the third side is expressed in whole centimeters. How many triangles does he have?
• Ruler and compass
Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°.
• Construct
Construct a rhombus ABCD, if the size of the diagonal AC is 6 cm and diagonal BD 8 cm long.

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