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.If the angle between two radii of a circle is $130^{\circ}$, then what is the angle between the tangents at the end points of radii at their point of intersection?
   • A.$62.5^{\circ}$
   • B.$45^{\circ}$
   • C.$35^{\circ}$
   • D.$50^{\circ}$
2. 2.Two circles touch each other internally. The tangents are drawn to the two circles from any point on the common tangent. Which of the following statements is true about these tangents?
   • A.The tangents from the point to both circles are equal in length.
   • B.The tangent to the larger circle is twice as long as the tangent to the smaller circle.
   • C.The tangent to the smaller circle is longer than the tangent to the larger circle.
   • D.The lengths of the tangents depend on the distance between the centers of the circles only.
3. 3.Triangle $ABC$ has sides $AB = 10 \text{ cm}$, $BC = 8 \text{ cm}$, and $AC = 6 \text{ cm}$. Three circles are drawn touching each other with the vertices as their centres. Find the radii of the three circles.
4. 4.In the given diagram $RT$ is a tangent touching the circle at $S$. If $\angle PST = 30^\circ$ and $\angle SPQ = 60^\circ$ then $\angle PSQ$ is equal to:
   • A.$40^{\circ}$
   • B.$30^{\circ}$
   • C.$60^{\circ}$
   • D.$90^{\circ}$
5. 5.What is value of angle $x$ in the given figure if $\angle PQR = 28^{\circ}$?
   • a.$56^{\circ}$
   • b.$31^{\circ}$
   • c.$28^{\circ}$
   • d.$62^{\circ}$