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.Tangent at P to the circumcircle of triangle PQR is drawn. If this tangent is parallel to side QR, which of the following must be true?
- A.ΔPQR is isosceles with PQ = PR
- B.ΔPQR is equilateral
- C.ΔPQR is scalene with all sides unequal
- D.ΔPQR is right-angled at P
-
2.In the given figure, PQ and PR are two equal chords of a circle. Which of the following statements correctly describes the relationship between the tangent at P and the line QR?
- A.The tangent at P is perpendicular to QR.
- B.The tangent at P is parallel to QR.
- C.The tangent at P intersects QR at a 45° angle.
- D.The tangent at P bisects QR.
-
3.In the given figure, MN is the common chord of two intersecting circles and AB is their common tangent. Which labelled point in the diagram is the midpoint of AB?
- A.Point M
- B.Point N
- C.Point P
- D.Point T
-
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 circle.
- A.4 cm
- B.6 cm
- C.8 cm
- D.10 cm
-
5.In figure $PQ$ is a chord of length $8\mathrm{cm}$ of a circle of radius $5\mathrm{cm}$. The tangents drawn at $P$ and $Q$ intersect at $T$. Find the length of $TP$.
Ready? Take the full 20-question test free — instant marking, no sign-up needed.
▶ Start free mock test