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 11
A chord of length 12 cm is at a distance of 5 cm from the center of a circle. Find the radius of the circle.
A circle has a radius of 8 cm. What is the length of the tangent from a point 17 cm from the center?
A circle passes through the points (1,2), (4,6), and (5,2). Find the equation of the circle.
A sector of a circle has a central angle of 60° and a radius of 6 cm. What is the area of the sector? (Use π = 3.14)
Explain the concept of concentric circles.
If the area of a circle is 314 cm2, what is its diameter? (Use π = 3.14)
If the area of a sector of a circle is 25π cm2 and the radius is 10 cm, what is the measure of the central angle in degrees?
A circle passes through the points (1,2), (4,6), and (5,2). Find the equation of the circle.
Which of the following is NOT a property of a tangent to a circle?
(1) It touches the circle at exactly one point.
(2) It passes through the center of the circle.
(3) It is perpendicular to the radius at the point of contact.
(4) The length of tangents from an external point to a circle are equal.
Which of the following is the correct definition of a secant of a circle?
(1) A line that touches the circle at exactly one point
(2) A line that passes through the center of the circle
(3) A line that intersects the circle at two points
(4) A line that does not intersect the circle
Which of the following is the general equation of a circle in the Cartesian plane?
(1) x2 + y2 + 2gx + 2fy + c = 0
(2) x2 + y2 + 2gx + 2fy = 0
(3) x2 + y2 = r2
(4) x2 + y2 + c = 0
Which of the following is the length of an arc of a circle of radius 10 cm subtending an angle of 90° at the center? (Use π = 3.14)
(1) 15.7 cm
(2) 7.85 cm
(3) 31.4 cm
(4) 5 cm
Fill in the blank: The locus of a point which moves such that its distance from a fixed point is constant is called a ______.
Fill in the blank: The measure of the angle subtended by an arc at the center is called the ______ angle.
Fill in the blank: The power of a point P with respect to a circle is defined as ______.
The angle subtended by a diameter at the circumference of a circle is always ______ degrees.
True or False: The center of a circle always lies inside the circle.
True or False: The length of a tangent from a point outside a circle to the circle 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 sum of the opposite angles of a cyclic quadrilateral is 180°.
