Circles
Math ⇒ Geometry
Circles starts at 7 and continues till grade 12.
QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Circles.
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See sample questions for grade 12
Describe the method to find the equation of a tangent to a circle at a given point.
Explain the concept of a cyclic quadrilateral and state one of its key properties.
Explain the difference between a secant and a chord of a circle.
State and prove the theorem: 'The tangents drawn from an external point to a circle are equal in length.'
A circle passes through the points (1,2), (4,6), and (5,2). Find the equation of the circle.
Which of the following best describes a concentric circle?
(1) Circles with the same radius
(2) Circles with the same center
(3) Circles with the same circumference
(4) Circles with the same area
Which of the following is NOT a property of a circle?
(1) All radii are equal
(2) The diameter is twice the radius
(3) The sum of the lengths of two tangents from an external point is equal to the diameter
(4) The center is equidistant from all points on the circle
Which of the following is the equation of a circle with center at (2, -3) and radius 5?
(1) (x + 2)2 + (y - 3)2 = 25
(2) (x - 2)2 + (y + 3)2 = 25
(3) (x - 2)2 + (y + 3)2 = 5
(4) (x + 2)2 + (y - 3)2 = 5
Which of the following is the locus of the center of all circles passing through two fixed points?
(1) The perpendicular bisector of the line segment joining the two points
(2) The line joining the two points
(3) The circle with diameter equal to the distance between the two points
(4) The tangent at one of the points
Fill in the blank: The angle subtended by a diameter at the circumference of a circle is always __________ degrees.
Fill in the blank: The maximum number of tangents that can be drawn from a point outside a circle is __________.
The general equation of a circle in the Cartesian plane is __________.
The length of a tangent from a point 13 cm from the center of a circle of radius 5 cm is __________ cm.
True or False: The area of a circle is directly proportional to the square of its radius.
True or False: The length of a tangent from a point outside a circle to the point of tangency is always equal for all tangents drawn from that point.
True or False: The perpendicular bisector of a chord passes through the center of the circle.
True or False: The power of a point with respect to a circle is always positive.
