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. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 12

A chord of a circle is 12 cm long and is at a distance of 5 cm from the center. What is the radius of the circle?

A circle has a diameter of 14 cm. What is its area? (Use π = 22/7)

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 45° and a radius of 8 cm. What is the area of the sector? (Use π = 3.14)

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.

If the area of a sector of a circle of radius 6 cm is 18π cm², what is the angle of the sector in degrees?

If the circumference of a circle is 44 cm, what is its radius? (Use π = 22/7)

If the equation of a circle is x² + y² - 6x + 8y + 9 = 0, what are the coordinates of its center?

If the equation of a circle is x² + y² = 49, what is the length of its diameter?

If the length of a chord is equal to the radius of the circle, what is the angle subtended by the chord at the center?

If two circles of radii 5 cm and 3 cm have their centers 8 cm apart, what is the length of their common external tangent?

State and prove the theorem: 'The tangents drawn from an external point to a circle are equal in length.'

State the converse of the theorem: 'The angle in a semicircle is a right angle.'

The equation x² + y² + 4x - 6y + 9 = 0 represents a circle. What is its radius?