Circles — Practice Quiz
ICSE · Class 10 · Mathematics
Try a 4-question quiz on Circles for ICSE Class 10 Mathematics: tap an answer to check it and see why. 40 questions in the full chapter test.
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In a circle with center O, an arc AB subtends an angle of 80° at the center. What angle will this arc subtend at a point P on the circle in the alternate segment?
A quadrilateral ABCD is inscribed in a circle. If ∠A = 70°, what is the measure of ∠C?
What is the angle in a semicircle?
From an external point P, two tangents PA and PB are drawn to a circle. If ∠APB = 60°, what is ∠AOB where O is the center?
Sample Questions
Which of the following are properties of tangents drawn from an external point to a circle?
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Equal in length, Subtend equal angles at center, Make equal angles with the line joining point to center
From an external point, tangents are: (1) equal in length, (2) subtend equal angles at center, (3) equally inclined to line joining point to center. They are neither parallel nor perpendicular to each other.
In triangle ABC inscribed in a circle, ∠BAC = 50°. What is the measure of arc BC?
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100°
The inscribed angle ∠BAC = 50° subtends arc BC. By the inscribed angle theorem, the arc measure is twice the inscribed angle. Therefore, arc BC = 2 × 50° = 100°.
Two chords AB and CD of a circle intersect at point P inside the circle. If PA = 6 cm, PB = 4 cm, and PC = 8 cm, find PD.
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3 cm
By the intersecting chords theorem: PA × PB = PC × PD. Substituting: 6 × 4 = 8 × PD, so 24 = 8 × PD, therefore PD = 24/8 = 3 cm.
A tangent PT and a secant PAB are drawn from external point P to a circle. If PA = 4 cm and AB = 5 cm, find the length of tangent PT.
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6 cm
By the tangent-secant theorem: PT² = PA × PB. Here PB = PA + AB = 4 + 5 = 9 cm. So PT² = 4 × 9 = 36, therefore PT = 6 cm.
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