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 given figure, chords AB and CD of a circle are produced to meet at O. Which of the following correctly identifies the relationship between the labelled triangles ΔODB and ΔOAC?
   • A.ΔODB and ΔOAC are congruent by SAS criterion.
   • B.ΔODB and ΔOAC are similar by AA similarity criterion.
   • C.ΔODB and ΔOAC are similar by SSS similarity criterion.
   • D.ΔODB and ΔOAC are neither congruent nor similar.
2. 2.In figure, $AT$ is a tangent to the circle with centre $O$ such that $OT = 4\mathrm{cm}$ and $\angle OTA = 30^{\circ}$. Then, $AT$ is equal to
   • A.$4\mathrm{cm}$
   • B.$2\mathrm{cm}$
   • C.$2\sqrt{3}\mathrm{cm}$
   • D.$4\sqrt{3}\mathrm{cm}$
3. 3.In the given diagram, the perpendicular bisector of chord AB is labelled CD. Which of the following statements correctly identifies the point through which CD must always pass?
   • A.The midpoint of chord AB
   • B.The centre of the circle, O
   • C.Any point on the circumference of the circle
   • D.The point where the tangent touches the circle
4. 4.If the angle between two tangents drawn from an external point $P$ to a circle of radius $a$ and centre $O$, is $60^\circ$, then find the length of $OP$.
5. 5.In the given figure, sides BC, CA, and AB of ΔABC touch a circle at points P, Q, and R respectively. If PC = 5 cm, AR = 4 cm, and RB = 6 cm, what is the perimeter of ΔABC?
   • A.24 cm
   • B.28 cm
   • C.30 cm
   • D.32 cm