ICSE Class 10 Circles (Tangent and Cyclic Properties) — Mock Test (2027)

Free online mock test for Circles (Tangent and Cyclic Properties) (ICSE Class 10 Mathematics) — 20 competency-based questions based on the latest CISCE 2027 syllabus, with instant marking. Try the samples below, then take the full test free.

Sample questions

1. 1.In the following figure $O$ is the centre of circle. what is the value of $x$?
   • a.$42^{\circ}$
   • b.$52^{\circ}$
   • c.$26^{\circ}$
   • d.$64^{\circ}$
2. 2.Prove that any four vertices of a regular pentagon are concyclic (lie on the same circle). Which of the following statements correctly justifies this?
   • A.A regular pentagon is inscribed in a circle, so any four of its vertices lie on the same circle.
   • B.A regular pentagon has equal sides, so any four vertices must lie on a circle with the same radius.
   • C.The sum of angles in any quadrilateral formed by four vertices is 360°, proving concyclicity.
   • D.Four vertices of a regular pentagon form a cyclic quadrilateral because opposite angles sum to 180°.
3. 3.In ΔPQR, PQ = 24 cm, QR = 7 cm and ∠PQR = 90°. The diagram shows the inscribed circle touching the sides. What is the radius of this inscribed circle?
   • A.2 cm
   • B.3 cm
   • C.4 cm
   • D.5 cm
4. 4.In the given figure, `` PQ is a transverse common tangent to two circles with centres A and B and of radii 5 cm and 3 cm respectively. If PQ intersects AB at C such that CP = 12 cm, which labelled segment corresponds to the length AB?
   • A.The distance between the two centres A and B along the line joining them
   • B.The length of the tangent segment PQ from P to Q
   • C.The perpendicular distance from centre A to the tangent PQ
   • D.The segment CP extended to the point where it meets the second circle
5. 5.In the given figure, a circle is inscribed in quadrilateral ABCD. If BC = 38 cm, BQ = 27 cm, DC = 25 cm and AD ⊥ DC, find the radius of the circle.