# Circle - high school - math problems

#### Number of problems found: 196

• 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?
• Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele
• Find the 13
Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4].
Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
• Dodecagon
Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.
• Circle and square
An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD.
• Chord BC
A circle k has the center at the point S = [0; 0]. Point A = [40; 30] lies on the circle k. How long is the chord BC if the center P of this chord has the coordinates: [- 14; 0]?
• Annulus
Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n.
• Suppose
Suppose you know that the length of a line segment is 15, x2=6, y2=14 and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not?
• A cell tower
A cell tower is located at coordinates (-5, -7) and has a circular range of 12 units. If Mr. XYZ is located at coordinates (4,5), will he be able to get a signal?
• Eq triangle minus arcs
In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts
• Inscribed circle
A circle is inscribed at the bottom wall of the cube with an edge (a = 1). What is the radius of the spherical surface that contains this circle and one of the vertex of the top cube base?
• 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.
• Circular railway
The railway connects in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C?
• Acceleration
Describe how the cyclist's acceleration changes on individual sections (sections AB plane, BC turn, CD plane, DA turn), which describes the trajectory in the shape of an eight at a constant speed. The speed on the cyclist's tachometer is constant
• Folding table
The folding kitchen table has a rectangular shape with an area of 168dm2 (side and is 14 dm long). If necessary, it can be enlarged by sliding two semi-circular plates (at sides b). How much percent will the table area increase? The result round to one-hu
• The triangle
The triangle is given by three vertices: A [0.0] B [-4.2] C [-6.0] Calculate V (intersection of heights), T (center of gravity), O - center of a circle circumscribed
• Annular area
The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area.
• RT sides
Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
• Mice
Mice consumed a circular hole in a slice of cheese. The cheese has the shape of a circular cut with a radius of 20 cm and an angle of 90 degrees. What percentage of the cheese ate mice if they made 20 holes with a diameter of 2 cm?

Do you have an interesting mathematical word problem that you can't solve? Submit a math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...

Circle Problems. Examples for secondary school students.