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.What is value of angle $x$ in the given figure if $\angle ABC = 110^\circ$?
   • a.$120^{\circ}$
   • b.$150^{\circ}$
   • c.$110^{\circ}$
   • d.$140^{\circ}$
2. 2.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
3. 3.In the given figure, if $\angle ACE = 43^\circ$ and $\angle CAF = 62^\circ$, find the values of $a$, $b$, and $c$.
   • A.$a = 75^\circ$, $b = 62^\circ$, $c = 43^\circ$
   • B.$a = 62^\circ$, $b = 75^\circ$, $c = 43^\circ$
   • C.$a = 43^\circ$, $b = 62^\circ$, $c = 75^\circ$
   • D.$a = 75^\circ$, $b = 43^\circ$, $c = 62^\circ$
4. 4.If the sides of a parallelogram touch a circle, which of the following must be true about the parallelogram?
   • A.It is a rectangle because all angles become 90 degrees.
   • B.It is a rhombus because all sides are equal.
   • C.It remains a general parallelogram with no special properties.
   • D.It is a square because all sides and angles are equal.
5. 5.(iii) In the given figure, tangent PT = 12.5 cm and PA = 10 cm; which labelled segment corresponds to the length AB = 5.625 cm?
   • A.The segment from P to the point where the tangent touches the circle
   • B.The part of the secant from A to B inside the circle
   • C.The entire secant from P through A and B
   • D.The radius drawn from the centre to point T