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, which labelled segment corresponds to the length that satisfies the relation TP² = TA · (TA + AB) when AT = 16 cm and AB = 12 cm?
   • A.TP = 8√7 cm
   • B.TP = 16 cm
   • C.TP = 20 cm
   • D.TP = 4√7 cm
2. 2.In the given figure if $\angle AOB = 125^{\circ}$, then $\angle COD$ is equal to
   • A.$62.5^{\circ}$
   • B.$45^{\circ}$
   • C.$35^{\circ}$
   • D.$55^{\circ}$
3. 3.In the given figure, ABC, AEQ and CEP are straight lines. Which of the following correctly identifies the pair of angles that are supplementary?
   • A.∠APE and ∠CQE, because they lie on a straight line ABC
   • B.∠APE and ∠CQE, because they are subtended by the same chord CE in a cyclic quadrilateral
   • C.∠AEQ and ∠CEP, because they form a linear pair
   • D.∠APE and ∠AEQ, because they are opposite angles in a cyclic quadrilateral
4. 4.Bisectors of vertex angles A, B and C of a triangle ABC intersect its circumcircle at the points D, E and F respectively. Which of the following correctly expresses the measure of angle EDF?
   • A.90° - 1/2 ∠A
   • B.90° + 1/2 ∠A
   • C.1/2 ∠A
   • D.180° - 1/2 ∠A
5. 5.$AB$ and $CD$ are two parallel chords of a circle such that $AB = 24 \, \text{cm}$ and $CD = 10 \, \text{cm}$. If the radius of the circle is $13 \, \text{cm}$, find the distance between the two chords.