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, MN is the common chord of two intersecting circles and AB is their common tangent. Which labelled point in the diagram is the midpoint of AB?
   • A.Point M
   • B.Point N
   • C.Point P
   • D.Point T
2. 2.In the given figure, XY is the diameter of the circle and PQ is a tangent to the circle at Y. If $\angle AXB = 50^{\circ}$ and $\angle ABX = 70^{\circ}$, which of the following correctly identifies $\angle BAY$ and $\angle APY$ in the diagram?
   • A.$\angle BAY = 20^\circ$ and $\angle APY = 50^\circ$
   • B.$\angle BAY = 30^\circ$ and $\angle APY = 70^\circ$
   • C.$\angle BAY = 40^\circ$ and $\angle APY = 50^\circ$
   • D.$\angle BAY = 20^\circ$ and $\angle APY = 40^\circ$
3. 3.Triangle ABC circumscribes a circle of radius 3 cm. The segments BD and DC are 6 cm and 9 cm respectively. If the area of ΔABC is 54 cm², what are the lengths of sides AB and AC?
   • A.AB = 8 cm, AC = 11 cm
   • B.AB = 9 cm, AC = 12 cm
   • C.AB = 10 cm, AC = 13 cm
   • D.AB = 7 cm, AC = 14 cm
4. 4.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.
5. 5.An isosceles $\Delta$ ABC is inscribed in a circle. If $\mathrm{AB} = \mathrm{AC} = 12\sqrt{5}$ cm and BC = 24 cm, find the radius of the circle.