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.
What to expect: This mock test covers key concepts from the Circles (Tangent and Cyclic Properties) chapter — including application-based and competency-focused questions aligned with how ICSE actually sets the paper.
Tip: Attempt without notes first to identify gaps, then review explanations for any wrong answers. Retake after a few days for best retention.
Sample questions
-
1.In the given figure, $C$ and $D$ are points on the semi-circle described on $BA$ as diameter. Given $\angle BAD = 70^{\circ}$ and $\angle DBC = 30^{\circ}$. What is the value of $\angle BDC$?
- A.$30^{\circ}$
- B.$35^{\circ}$
- C.$40^{\circ}$
- D.$45^{\circ}$
-
2.Prove that any four vertices of a regular pentagon are concyclic (lie on the same circle). Which of the following statements correctly justifies this?
- A.A regular pentagon is inscribed in a circle, so any four of its vertices lie on the same circle.
- B.A regular pentagon has equal sides, so any four vertices must lie on a circle with the same radius.
- C.The sum of angles in any quadrilateral formed by four vertices is 360°, proving concyclicity.
- D.Four vertices of a regular pentagon form a cyclic quadrilateral because opposite angles sum to 180°.
-
3.In the given figure, AB is the diameter of the circle, with centre O, and AT is the tangent. Calculate the numerical value of x.
-
4.ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circles are drawn touching each other with the vertices as their centres. The diagram below shows the labelled radii of the circles centered at A, B, and C as r₁, r₂, and r₃ respectively.
Which of the following correctly identifies the radii of the circles centered at A, B, and C?- A.r₁ = 4 cm, r₂ = 6 cm, r₃ = 2 cm
- B.r₁ = 5 cm, r₂ = 5 cm, r₃ = 3 cm
- C.r₁ = 3 cm, r₂ = 7 cm, r₃ = 1 cm
- D.r₁ = 6 cm, r₂ = 4 cm, r₃ = 2 cm
-
5.In the given circle with diameter AB, find the value of $x$.
Ready? Take the full 20-question test free — instant marking, no sign-up needed.
▶ Start free mock test