Maths · Chapter 25
Geometry II · Circles & Quadrilaterals PYQs
Chords, angles, tangents, cyclic quadrilaterals and polygons: a handful of theorems that open almost every geometry question after triangles.
Chords: perpendicular from the centre, equal and parallel chords 8 PYQs
- A chord of length 16 cm is 6 cm away from the centre of a circle. Find the radius of the circle.SSC Selection Post 2026 · 21 Sep 2026
- Let C ₁and C₂ be two concentric circles with centre O. Let AB be a chord on C₁ the larger circle such that AB touches C₂ at the point P. Then which…RRB NTPC 2026 · 24 Mar 2026
- In a circle with centre O and radius 13 cm, two parallel chords AB and CD are drawn on opposite sides of the centre. If AB = 10 cm and CD = 24 cm,…SSC Selection Post 2026 · 19 Sep 2026
- In a circle of radius 17 cm, two parallel chords are drawn on opposite sides of the centre. One chord is 16 cm long and the distance between them is…SSC Selection Post 2026 · 17 Sep 2026
- Two parallel chords are drawn on opposite sides of the centre of a circle of diameter 30 cm. One chord has length 24 cm, and the perpendicular…SSC Selection Post 2026 · 22 Sep 2026
- In a circle with a diameter of 34 cm, two parallel chords are drawn on opposite sides of the centre. The length of one chord is 30 cm, and the…SSC Selection Post 2026 · 24 Sep 2026
- In a circle with centre O, AD is a diameter and AC is a chord. Point B is on AD such that OB = 7 cm and BC = 9 cm. If ∠OBC = 60°, find the radius of…SSC Selection Post 2026 · 24 Sep 2026
- Two concentric circles have radii of 15 cm and 17 cm. Find out the length of the chord of the larger circle that is tangent to the smaller circle.RRB NTPC 2026 · 22 Mar 2026
Angles in a circle: centre, circumference, same segment, semicircle 3 PYQs
- Points C and D lie on the same segment of a circle with chord AB. If ∠ACB = 55°, what is ∠ADB?SSC Selection Post 2026 · 23 Sep 2026
- A chord AB subtends an angle of 70° at the centre of the circle. Find the angle subtended by the same chord at a point on the major arc of the circle.SSC Selection Post 2026 · 21 Sep 2026
- Let C be a circle with centre O and AB be a minor arc on C. Let S be a point on the minor arc AB. If AB subtends an angle 120° at O, then find the…RRB NTPC 2026 · 22 Mar 2026
Chords meeting inside or outside the circle: the angle between them 1 PYQs
Cyclic quadrilateral 2 PYQs
- In a cyclic quadrilateral, two opposite angles are (2x + 10)° and (3x − 5)°. Find the larger of these two opposite angles.SSC Selection Post 2026 · 19 Sep 2026
- A chord of a circle subtends an angle of 40° at a point on the circle. Find the angle subtended by the same chord at a point on the opposite segment.SSC Selection Post 2026 · 24 Sep 2026
Tangent from an external point: length and angles 7 PYQs
- A point P is at a distance of 13 cm from the centre of a circle. If the radius of the circle is 5 cm, what is the length of the tangent segment…SSC Selection Post 2026 · 19 Sep 2026
- Two tangents are drawn from an external point T to a circle with centre O, touching at A and B. If ∠AOB = 120°, what is ∠ATB?SSC Selection Post 2026 · 21 Sep 2026
- A tangent line drawn from a point outside a circle has a length equal to the circle's radius. Find the angle formed by the radius at the point of…Delhi Police 2026 · 09 Jan 2026
- PR and PS are the two tangents drawn from an external point P to the circle of radius 10 cm with centre O. Find the perimeter of quadrilateral ORPS…Delhi Police 2026 · 12 Jan 2026
- In a circle with centre O, PA and PB are tangents touching the circle at A and B respectively. Point C lies on the major arc AB. If ∠ACB = 50°, find…SSC Selection Post 2026 · 25 Sep 2026
- Tangents PT and PS are drawn from an external point P to a circle of radius 5 cm. If the distance from P to the centre O is 13 cm, find the area of…SSC Selection Post 2026 · 24 Sep 2026
- Two tangents AB and AC are drawn from an external point A to a circle with centre O. If AB = 30 cm and BC = 24 cm, then find the radius of the…RRB NTPC 2026 · 17 Mar 2026