Circles
69 CDS Mathematics previous year questions (PYQs) from 21 papers, 2016 to 2026, with answers and worked solutions.
About this chapter
- Difficulty: 7 easy · 44 moderate · 18 hard.
- Most-asked subtopics: Chords and Perpendiculars (15), Angles in a Circle (13), Tangents from an External Point (11).
- Updated 20 September 2026.
#1Chords and Perpendiculars
#2Chords and Perpendiculars
#3Chords and Perpendiculars
#4Chords and Perpendiculars
#5Chords and Perpendiculars
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#6Chords and Perpendiculars
#7Chords and Perpendiculars
#8Chords and Perpendiculars
#9Chords and Perpendiculars
- Set · 2 questionsTwo parallel chords AB and CD of a circle are of lengths 60 cm and 80 cm respectively. They are on the same side of the centre O and 10 cm apart.
#10Chords and Perpendiculars
#11Chords and Perpendiculars
#12Chords and Perpendiculars
- Set · 1 questionConsider the following for the next ten (10) items that follow : Each item contains a Question followed by two Statements. Answer each item using the following instructions :
#13Chords and Perpendiculars
#14Chords and Perpendiculars
#15Chords and Perpendiculars
#16Angles in a Circle
#17Angles in a Circle
#18Angles in a Circle
#19Angles in a Circle
#20Angles in a Circle
- Set · 2 questionsConsider the following for the next two (02) items that follow : is a diameter of a circle with centre . Radius is perpendicular to . Let be any point on arc .
#21Angles in a Circle
#22Angles in a Circle
#23Angles in a Circle
#24Angles in a Circle
#25Angles in a Circle
- Set · 2 questionsConsider the following for the next two (02) items that follow : In the following figure, a triangle ABC is inscribed in a circle with centre at O. Let and . Further, OB = BQ.
- CDS · 2023 · CDS (I) 2023 — Elementary Mathematics · Q99ModerateHas image
#26Angles in a Circle
- CDS · 2023 · CDS (I) 2023 — Elementary Mathematics · Q100ModerateHas image
#27Angles in a Circle
#28Angles in a Circle
- Set · 3 questionsFor the next three (03) items that follow : The centre O of a circle inside a triangle ABC is at a distance of 13 cm from each of the vertices of the triangle. The diameter of the circle is 10 cm and the circle touches only two sides of the triangle, AB and AC.
#29Circumcircle and Locus
#30Circumcircle and Locus
#31Circumcircle and Locus
#32Circumcircle and Locus
#33Circumcircle and Locus
#34Circumcircle and Locus
#35Circumcircle and Locus
- Set · 1 questionConsider the following for the next three (03) items that follow : A triangle ABC with sides AB = 15 cm, BC = 9 cm, CA = 12 cm is inscribed in a circle.
#36Circumcircle and Locus
- Set · 1 questionFor the next ten (10) items that follow : Each item contains a Question followed by two Statements. Answer each item using the following instructions :
#37Circumcircle and Locus
#38Tangents from an External Point
#39Tangents from an External Point
#40Tangents from an External Point
- CDS · 2018 · CDS (I) 2018 — Elementary Mathematics · Q96ModerateHas image
#41Tangents from an External Point
- CDS · 2018 · CDS (I) 2018 — Elementary Mathematics · Q99ModerateHas image
#42Tangents from an External Point
#43Tangents from an External Point
- Set · 1 questionConsider the following for the next ten (10) items that follow : Each item contains a Question followed by two Statements. Answer each item using the following instructions :
#44Tangents from an External Point
- Set · 3 questionsLet be a chord of length 16 cm of a circle with centre at and radius 10 cm. The tangents at and intersect at a point . Further, intersects perpendicularly at .
#45Tangents from an External Point
#46Tangents from an External Point
#47Tangents from an External Point
#48Tangents from an External Point
- Set · 1 questionFor the next three (03) items that follow : A circle with centre O passes through the vertex A of an equilateral triangle ABC and touches BC at its midpoint M. The circle cuts AB at D and AC at E.
#49Intersecting Chords and Power of a Point
#50Intersecting Chords and Power of a Point
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