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.Two circles intersect in points P and Q. A secant passing through P intersects the circles in A and B respectively. Tangents to the circles at A and B intersect at T. Which of the following statements correctly explains why points A, Q, B, and T lie on the same circle?
- A.By the tangent-secant theorem, ∠TAP = ∠AQP and ∠TBP = ∠BQP, leading to ∠ATB + ∠AQB = 180°, proving quadrilateral AQBT is cyclic.
- B.Points A, Q, B, and T form a parallelogram, ensuring opposite angles sum to 180° and thus lie on a circle.
- C.Since T is the intersection of tangents at A and B, ∠ATB is always 90°, making AQBT a cyclic quadrilateral.
- D.The secant through P ensures ∠AQB = ∠APB, and since ∠ATB = ∠APB, the points must lie on a circle.
-
2.In the given figure, two chords of lengths $24 \text{ cm}$ and $18 \text{ cm}$ are drawn. If $OA = OC = 15 \text{ cm}$, find the length of $MN$ where $OM \perp AB$ and $ON \perp CD$.
-
3.In given figure if $\angle DBC = 70^{\circ}$ and $\angle BAC = 40^{\circ}$, what is the value of $\angle BCD$?
- A.$70^{\circ}$
- B.$60^{\circ}$
- C.$90^{\circ}$
- D.$65^{\circ}$
-
4.In the given diagram, a chord AB of length 16 cm is drawn in a circle with centre O and radius 10 cm. OM is perpendicular to AB, meeting it at M. Which labelled segment represents the distance of the chord from the centre of the circle?
- A.OA
- B.OM
- C.AM
- D.AB
-
5.In the figure given below, AC is a transverse common tangent to two circles with centres P and Q and of radii 6 cm and 3 cm respectively. Given that AB = 8 cm, which labelled segment in the diagram corresponds to the perpendicular distance used to calculate PQ using the Pythagorean theorem?
- A.The segment joining the points of tangency M and N
- B.The difference in radii (PM - QN) = 3 cm
- C.The entire length of the tangent AC
- D.The radius of the larger circle PM = 6 cm
Ready? Take the full 20-question test free — instant marking, no sign-up needed.
▶ Start free mock test