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
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1.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
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2.Three circles touch each other externally. A triangle is formed when the centres of these circles are joined together. Find the radii of the circles, if the sides of the triangle formed are 6 cm, 8 cm and 9 cm.
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3.From a point $T$ outside a circle of centre $O$, tangents $TP$ and $TQ$ are drawn to the circle. Which of the following statements correctly describes the relationship between $OT$ and the line segment $PQ$?
- A.$OT$ bisects $PQ$ but is not perpendicular to it.
- B.$OT$ is perpendicular to $PQ$ but does not bisect it.
- C.$OT$ is the right bisector of $PQ$.
- D.$OT$ neither bisects nor is perpendicular to $PQ$.
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4.In the given circle with centre O, $\angle ABC = 100^{\circ}$, $\angle ACD = 40^{\circ}$ and CT is a tangent to the circle at C. Which labelled angle corresponds to $\angle DCT$ in the diagram?
- A.The angle between chord AC and tangent CT at point C
- B.The angle between chord BC and tangent CT at point C
- C.The angle subtended by chord AD at the circumference
- D.The angle between radius OC and tangent CT at point C
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5.An equilateral triangle of side 9 cm is inscribed in a circle. Find the radius of the circle.
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