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 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?

If the circumference of a circle is 31.4 cm, what is its radius? (Use π = 3.14)

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 tangent from a point 13 cm away from the center of a circle is 12 cm, what is the radius of the circle?

If two circles of radii 5 cm and 3 cm touch each other externally, what is the distance between their centers?

State the formula for the length of a chord of a circle in terms of the radius r and the perpendicular distance d from the center to the chord.

State the relationship between the angle at the center and the angle at the circumference subtended by the same arc.

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

What is the equation of a circle with center at (3, -2) and radius 5?

A circle has the equation x² + y² + 4x - 8y + 4 = 0. Find the coordinates of the center and the length of the radius.

A circle passes through the points (2,3), (6,7), and (8,3). Find the center and radius of the circle.

A circle with center O has a chord AB of length 16 cm. The distance from O to AB is 6 cm. Calculate the radius of the circle.

Given the equation of a circle as x² + y² + 2gx + 2fy + c = 0, derive the formula for the length of the tangent from a point P(x₁, y₁) to the circle.