Circles
24 solved questions from Class 10 Mathematics, each with the full working. Tap any question to see the step-by-step solution.
- 1 From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP = 13 cm and the radius of the circle is 5 cm, what is the length of each tangent segment PA (or PB)? medium MCQ 2 marks Length of tangent from external point
- 2 The central angle of a sector of a circle is 45° and the radius of the circle is 14 cm. Find (i) the length of the arc of the sector, and (ii) the area of the sector. Give your answers in cm and cm^2 respectively, correct to two decimal places. medium 2 marks Sector area and arc length
- 3 A circle has radius 10 cm. The distance of a chord from the centre is 6 cm. Find the length of the chord. easy 1 mark Chord length from distance to centre
- 4 Two chords AB and CD of a circle intersect at point E inside the circle. If AE = 4 cm, EB = 6 cm, CE = 3 cm and the radius of the circle is 10 cm, find the length of ED. hard 3 marks Intersecting chords theorem
- 5 In a circle with centre O, a chord AB subtends an angle of 60° at the centre. A tangent at point A meets the extension of chord AB at point T. What is the measure of ∠ TBA? easy MCQ 1 mark Angle between tangent and chord
- 6 Find the length of a chord of a circle whose radius is 13 cm and whose distance from the centre is 5 cm. easy 1 mark Chord length from distance
- 7 Two chords AB and CD of a circle intersect at point E inside the circle. If AE = 3 cm, EB = 5 cm and CE = 2 cm, find ED. easy MCQ 1 mark Intersecting chords theorem
- 8 From a point P outside a circle, a tangent PA is drawn. If OP = 15 cm and the radius of the circle is 8 cm, find the length of PA. medium 2 marks Length of tangent from external point
- 9 Find the area of a sector of a circle whose radius is 8 cm and whose central angle is 75°. medium 2 marks Area of a sector
- 10 In a circle with centre O, a chord AB subtends an angle of 80° at the centre. A tangent at B meets the extension of AB at T. Find the measure of ∠ ATB. hard 5 marks Angle between chord and tangent
- 11 A circle has radius 15 cm. The perpendicular distance of a chord from the centre is 9 cm. What is the length of the chord? easy MCQ 1 mark Chord length from its distance from centre
- 12 What is the sum of all interior angles of a triangle? medium MCQ Angle Sum Property
- 13 What is the sum of interior angles of a quadrilateral? medium MCQ Polygon Angles
- 14 In a right triangle with legs 3 cm and 4 cm, find hypotenuse length. medium MCQ Pythagoras Theorem
- 15 How many tangents can be drawn to a circle from an external point? medium MCQ Tangents to Circle
- 16 What is the angle between a tangent and the radius at the point of contact? medium MCQ Tangent Properties
- 17 Two triangles are similar if their corresponding sides are in ____. medium MCQ Similar Triangles
- 18 Find the perimeter of a square with side length 6 cm. medium MCQ Perimeter of Square
- 19 What is the formula for area of a circle with radius r? medium MCQ Area of Circle
- 20 If diameter of a circle is 14 cm, what is its radius? medium MCQ Circle Definitions
- 21 State Pythagoras Theorem for a right-angled triangle. medium MCQ Pythagoras Theorem
- 22 What is the domain, range, or fundamental theorem introduced in 'Circles' (Class 10 Mathematics)? medium MCQ Functions & Theorems
- 23 What is the derivative or integral formula associated with 'Circles'? medium MCQ Calculus & Formulae
- 24 How do you find the solution set or optimum value in 'Circles'? medium MCQ Problem Solving & Optimization