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 $O$ is the centre of the circle. What are the values of $x$ and $y$?
   • A.$85^{\circ}$ and $5^{\circ}$
   • B.$5^{\circ}$ and $85^{\circ}$
   • C.$70^{\circ}$ and $15^{\circ}$
   • D.$15^{\circ}$ and $70^{\circ}$
2. 2.Two circles intersect at P and Q. Through P diameters PA and PB of the two circles are drawn. Which of the following statements correctly explains why the points A, Q and B are collinear?
   • A.∠AQP and ∠BQP are both 90° because they are angles in a semicircle, making ∠AQB = 180°.
   • B.Points A, Q, and B lie on the same straight line because PA and PB are equal in length.
   • C.∠AQB is 90° since it is formed by the intersection of two diameters.
   • D.A, Q, and B are collinear because PQ is the common chord of the two circles.
3. 3.In the given figure, O is the centre of the circle and ∠PBA = 45°. What is the value of ∠PQB?
   • A.30°
   • B.45°
   • C.60°
   • D.90°
4. 4.Two circles intersect at P and Q. Through P, a straight line APB is drawn to meet the circles in A and B. Through Q, a straight line is drawn to meet the circles at C and D. In the diagram below, which labelled angle relationship proves that AC is parallel to BD?
   • A.∠CAP = ∠CQP (angles in the same segment)
   • B.∠CAP = ∠QDB (angles in the same segment)
   • C.∠APQ = ∠BQD (vertically opposite angles)
   • D.∠ACQ = ∠BDQ (corresponding angles)
5. 5.In the given diagram of a cyclic quadrilateral ABCD, sides AB and CD are parallel. Identify which labelled segment must be equal to AD based on the properties of cyclic quadrilaterals and parallel lines.
   • A.BC
   • B.AC
   • C.BD
   • D.AB