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.Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base. Which of the following correctly explains why this is true?
   • A.The circle passes through the third vertex and creates two congruent triangles, bisecting the base.
   • B.The circle divides the base into two equal parts because the diameter is the longest chord.
   • C.The base is bisected because the circle's radius is equal to half the base length.
   • D.The circle intersects the base at its midpoint due to the triangle's symmetry alone.
2. 2.In the given figure, two chords AB and CD of a circle intersect at a point P. If AB = CD, which of the following statements about the arcs is correct?
   • A.Arc AD is equal to arc BC
   • B.Arc AC is equal to arc BD
   • C.Arc AD is twice the length of arc BC
   • D.Arc AB is equal to arc CD but arc AD is not equal to arc BC
3. 3.In the given figure $O$ is the centre of the circle and given that $AB = BC$. What are the values of $x$ and $y$?
   • A.$45^{\circ}$ and $65^{\circ}$
   • B.$20^{\circ}$ and $70^{\circ}$
   • C.$70^{\circ}$ and $20^{\circ}$
   • D.$65^{\circ}$ and $45^{\circ}$
4. 4.Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner.
5. 5.In the given figure, $AB$ and $CD$ are two chords of a circle intersecting at $P$ such that $AP = CP$. Which of the following must be true?
   • A.$AB = 2 \times CD$
   • B.$AB = CD$
   • C.$AP = BD$
   • D.$\angle APD = \angle BPC$ only