Circle - high school - practice problems
Number of problems found: 284
- The length 17
The length of one of two chords of a circle is 12cm. If the chords are 6cm and 7cm, respectively, away from the center of the circle, calculate the length of the second chord. - A cone 3
A cone has a diameter of x cm and a slant height of y cm. A square pyramid has a base side length of x cm and a slant height of y cm. Which has the greater surface area? Explain. - Find all 2
Find all the complex solutions (write the answer in the form x+iy) of the system. {|z-12|/|z-8i|=5/3 ; |z-4|=|z-8| - Subtended 83194
A circle k with a center at point S and a radius of 6 cm is given. Calculate the size of the central angle subtended by a chord 10 cm long.
- 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? - Semicircle 82687
If the shell of a cone is a semicircle, then the diameter of the cone's base is equal to its side's length. Prove it. - 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.
- Quadrilateral 82395
The points ABC lie on the circle k(S, r) such that the angle at B is obtuse. How large must the angle at vertex B of quadrilateral SCBA be so that this angle is three times greater than the interior angle ASC of the same quadrilateral? - 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, - Determine 82341
Determine the equation of the circle that is the set of all points of the plane that are twice as far from the point [3,7] as they are from the point [0,1]. - Equation 81932
Write the general equation of a circle with point S(2;5) and point B(5;6) lying on this circle. - Circumscribed 81759
In triangle ABC, we know a = 4 cm, b = 6 cm, γ = 60°. Calculate the area and radius of the inscribed and circumscribed circle.
- Quatrefoil 81138
Gothic quatrefoil is an ornament in which four identical touching smaller circles are inscribed in a larger circle, as you can see in the picture. The radius of the great circle is one meter. Calculate the radius of the smaller circle in meters. - Circle's 81078
The chord of a circle is 233 long, and the length of the circular arc above the chord is 235. What is the circle's radius, and what is the central angle of the circular arc? - Difference 80618
A regular hexagon is described and inscribed in a circle. The difference between its areas is 8√3. Find the circle's radius. - Circumscribing 80498
Given is an acute-angled triangle ABC. On the half lines opposite to BA and CA lie successively the points D and E such that |BD| = |AC| and |CE| = |AB|. Prove that the center of the circle circumscribing triangle ADE lies on the circle circumscribing tri - Equation of the circle
Find an equation of the circle whose diameter has endpoints (1,-4) and (3,2).
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