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 given figure, ABCD is a cyclic quadrilateral. AF is drawn parallel to CB and DA is produced to point E. If $\angle ADC = 92^{\circ}$, $\angle FAE = 20^{\circ}$; which labelled angle in the diagram corresponds to $\angle BCD$ and what is its measure?
- A.$\angle BCD = 88^{\circ}$ (angle opposite to $\angle ADC$ in the cyclic quadrilateral)
- B.$\angle BCD = 108^{\circ}$ (exterior angle formed by extending DA and using parallel lines)
- C.$\angle BCD = 72^{\circ}$ (sum of $\angle FAE$ and $\angle ADC$ subtracted from $180^{\circ}$)
- D.$\angle BCD = 68^{\circ}$ (difference between $\angle ADC$ and $\angle FAE$)
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2.In the given figure, two chords $AB = 24$ cm and $CD = 18$ cm are drawn in a circle with radius $15$ cm. If $OM \perp AB$ and $ON \perp CD$, find the length of $MN$.
- A.$15$ cm
- B.$21$ cm
- C.$24$ cm
- D.$27$ cm
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3.In the given figure, O is the centre of the circle. Identify the value of angle **a** in
based on the labelled parts and circle properties.
Which of the following correctly represents the measure of angle **a**?- A.Equal to the angle subtended by the same arc at the circumference
- B.Twice the angle subtended by the same arc at the circumference
- C.Half the angle subtended by the same arc at the center
- D.Equal to the angle between the tangent and the chord at the point of contact
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4.Find the unknown length x in the following figure: (i)
(ii) 
(iii) 
(iv) 
(v) 
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5.In the given figure $O$ is the centre of the circle.
Statement 1: The value of angle $x$ is $45^{\circ}$.
Statement 2: The value of angle $y$ is $75^{\circ}$.
Which of the following is valid?- A.Both statements are true.
- B.Both statements are false.
- C.Statement 1 is true and statement 2 is false
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