Line + circle - practice problems
Number of problems found: 73
- Construct 83195
Two line segments of different lengths are given. Construct a circle k so that both line segments are its chords. - Parametrically 82990
Calculate the sum of the x-coordinates of the intersections of the circle given by the equation (x - 1)²+ y² = 1 and the line given parametrically x = t, y = t , where t∈R. - Coordinate 82855
What is the ratio of the distance of the nearest and farthest point of the circle described by the equation x2+y2-16x-12y+75=0 from the origin of the coordinate system? - Vertex of the rectangle
Determine the coordinates of the vertex of the rectangle inscribed in the circle x²+y² -2x-4y-20=0 if you know that one of its sides lies on the line p: x+2y=0 - Circle - analytics geometry
Write the equation of the circle that passes through the points Q[3.5] R[2.6] and has its center on the line 2x+3y-4=0. - Determine 82394
Determine the equation of the circle that passes through the point M(-1,2) and N( 3,0) and whose center lies on the line p: x=-3+t, y=-1+t, - Construction: 81894
Construct a rhombus that has a side length of 5 cm and a height of 4.5 cm. Outline: Analysis: Construction: Method: - Sprinkler 80801
A sprinkler is located in the park at a distance of 3m from the sidewalk. Water blasted up to a distance of max. 5m. What is the maximum length of the sidewalk it will cover? - Hypotenuse 78844
Construct triangle KLM if side m=6.5cm, hypotenuse tm=4cm, height to side m: vm=3.2cm - Parallelogram 72044
Assembly parallelogram ABCD: AB = 4.8cm, va = 3cm, BC = 4cm. Calculate the circuit. Make a sketch. - Arbitrary 69194
There are ten arbitrary points in the plane. How many circles can we make from them? - Hypotenuse 65744
Construct a right triangle ABC with the hypotenuse AB: a) | AB | = 72 mm, | BC | = 51 mm b) | AB | = 58 mm, | AC | = 42 mm - Calculate 58953
Calculate the area of a circular line if the radius r = 80 cm and the central angle is α = 110 °. - Instructions: 56651
Divide the line segment AB into three equal parts. Instructions: Construct an equilateral triangle ABC and find its center (e.g., the described circles). - Construction 55311
Construct a KLM triangle where side k is 6.7 cm, the line to the k side is 4.1 cm, and the LKM angle is 63 degrees. Write the construction procedure. - Touch circle
Point A has a distance (A, k) = 10 cm from a circle k with radius r = 4 cm and center S. Calculate: a) the distance of point A from the point of contact T if the tangent to the circle is drawn from point A b) the distance of the contact point T from the l - Determine 54881
On the tourist map with a scale of 1:50000, the section of the railway line between Bobrová Lhota and Javořiště is replaced by an arc of a circle with a radius of 6 cm. The arc is 90°. Determine the actual length of the track between the two villages. - Solutions 45511
Two parallel chords in a circle with a radius of 6 cm have lengths of 6 cm and 10 cm. Calculate their distance from each other. Find both solutions. - Construction 32971
There is any circle k that does not have a marked center. Use a suitable construction to find the center of the circle k. Try on two different circles. - Five circles
On the line segment CD = 6 there are five circles with one radius at regular intervals. Find the lengths of the lines AD, AF, AG, BD, and CE.
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