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.Two circles touch each other internally. The tangents are drawn to the two circles from any point on the common tangent. Which of the following statements is true about these tangents?
- A.The tangents from the point to both circles are equal in length.
- B.The tangent to the larger circle is twice as long as the tangent to the smaller circle.
- C.The tangent to the smaller circle is longer than the tangent to the larger circle.
- D.The lengths of the tangents depend on the distance between the centers of the circles only.
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2.In the given circle with centre O, ∠ABC = 100°, ∠ACD = 40°, and CT is a tangent to the circle at C. What are the measures of ∠ADC and ∠DCT?
- A.∠ADC = 80°, ∠DCT = 50°
- B.∠ADC = 80°, ∠DCT = 60°
- C.∠ADC = 70°, ∠DCT = 60°
- D.∠ADC = 90°, ∠DCT = 40°
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3.A circle with centre O and diameter AB has chord AD. Another circle is drawn with AO as diameter to cut AD at C. Which relationship holds true?
- A.BD = OC
- B.BD = 2OC
- C.OC = 2BD
- D.BD = 3OC
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4.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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5.In the given figure, chords AB and CD, when extended, meet at X. AB = 4 cm, BX = 6 cm, and XD = 5 cm. What is the length of CD?
- A.5 cm
- B.7 cm
- C.9 cm
- D.11 cm
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