Geometry construction - practice problems - page 5 of 10
Number of problems found: 185
- Rectangular trapezoid ZIMA
I have a rectangular trapezoid ZIMA (the right angle at the top of Z. ZIMA = winter in English) ZI-7cm, ZM-5cm, AM-3.5cm, and we have to write the procedure to construct this trapezoid. - Triangle circle construction
The vertices of the triangle ABC lie on the circle k. The circle k is divided into three parts in a ratio of 1:2:3. Construct this triangle. - Square central symmetry
Draw a square KLMN, a point R that is a point of the square, and a point S that is not a point of this square. Draw the image of the square KLMN in central symmetry with the center : a) at point s b) at point M c) at point R - Geometric drawing exercise
Draw in one picture: a) straight line RZ b) YZ for which YZ is perpendicular to RZ c) the half-line RS diverging with YZ and with the line RZ d) point F, which lies on YZ outside the already selected points e) point H, which lies on the half-line RS and t - 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. - Cube construction
A 2×2×2 cube will be constructed using four white and four black unit cube. How many different cubes can be constructed in this way? ( Two cubes are not different if one can be obtained by rotating the other. ) - 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 line c, that intersect the two parallel lines. Draw a circle that touches all lines at the same time. - Construct rhombus - MO
Construct the diamond ABCD so that its diagonal BD is 8 cm and the distance of apex B from the line AD is 5 cm. Specify all possibilities. How long is a side of a rhombus? - Calculate sides
In the triangle, the side length AB = 6 cm, the height to side c = 5 cm, and the angle BCA = 35°. Calculate sides a b. - Circle line tangent
Given a circle k(O; 2.5 cm), a line p: /Op/=4 cm, a point T: T belongs to p and at the same time /OT/=4.5 cm. We must find all the circles that will touch the circle k and the line p at point T. - Circle position sketch
Sketch the relative position of the circles k1 (S1, r1 = 5cm) and k2 (S2, r2 = 3cm) and k / S1S2 / = 0 cm and give its name. - The pool - optimization
A block-shaped pool with a volume of 200 m³ is to be built in the recreation area. Its length should be 4 times the width, while the price of 1 m² of the pool bottom is 2 times cheaper than 1 m² of the pool wall. What dimensions must the pool have to make - Dividing a Circle
Draw a circle k, r = 4cm, and divide it into two parts in a ratio of 1:5. - Rectangle drawing calculation
Draw rectangles. Color them and calculate the circuits and areas. KLMN: KL = 5CM LM = 3CM rectangle OPQR OP = 4cm PQ = 3.5cm - Square drawing calculation
Draw squares. Color them and calculate the perimeter and areas square ABCD a = 3cm square EFGH b = 4cm - Triangle Geometry Proof
On side AB of triangle ABC, points D and E are given such that |AD| = |DE| = |EB|. Points A and B are the midpoints of segments CF and CG. Line CD intersects line FB at point I, and line CE intersects line AG at point J. Prove that the intersection of lin - Point construction
Given an isosceles right triangle ABS with base AB. On a circle centered at point S and passing through points A and B, point C lies such that triangle ABC is isosceles. Determine how many points C satisfy the given conditions and construct all such point - Construct
Construct a triangle ABC inscribed circle with a radius r = 2 cm and an angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction, and description. - Boat in the lake
A boatman walks along the ship's deck at a constant speed of 5 km/h in a direction that forms an angle of 60° with the direction of the ship's speed. The boat moves with respect to the lake's calm surface at a constant speed of 10 km/h. Determine graphica
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