ICSE question bank

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18 questions

Answer available
Class 10 · Mathematics · Circles
In a cyclic quadrilateral ABCD, angle A = 70°. Find angle C.
2 marksEasyNumerical
Answer available
Class 10 · Mathematics · Circles
In a cyclic quadrilateral, the exterior angle at a vertex is equal to:
1 markMediumMCQ
Answer available
Class 10 · Mathematics · Circles
A tangent to a circle of radius 8 cm is drawn from a point 17 cm from the centre. Find the length of the tangent.
3 marksMediumNumerical
Answer available
Class 10 · Mathematics · Circles
PT is a tangent from an external point P to a circle, and PAB is a secant through P meeting the circle at A and B. If PT = 6 cm and PA = 4 cm, find PB.
3 marksMediumNumerical
Answer available
Class 10 · Mathematics · Circles
In a circle of radius 13 cm, a chord is at a distance of 5 cm from the centre. Find the length of the chord.
3 marksMediumNumerical
Answer available
Class 10 · Mathematics · Circles
From an external point P two tangents PA and PB are drawn to a circle with centre O. If angle APB = 60°, find angle AOB.
3 marksMediumNumerical
Answer available
Class 10 · Mathematics · Circles
The angle subtended by a diameter at any point on the circle is:
1 markEasyMCQ
Answer available
Class 10 · Mathematics · Circles
Draw a circle with centre O and a chord AB. Mark a point C on the major arc and a point D on the minor arc. Show on your diagram why angle ACB and angle ADB are supplementary.
3 marksMediumDiagram based
Answer available
Class 10 · Mathematics · Circles
In a circle with centre O, AB is a diameter and C is a point on the circle. If angle CAB = 35°, find angle ACB and angle ABC.
4 marksHardStructured
Answer available
Class 10 · Mathematics · Circles
Two chords AB and CD of a circle intersect inside the circle at P. If PA = 4 cm, PB = 6 cm and PC = 3 cm, find PD.
3 marksMediumNumerical
Answer available
Class 10 · Mathematics · Circles
In a circle with centre O, chord AB is produced to a point P outside the circle, and PT is a tangent from P touching the circle at T. If PA = 5 cm and AB = 7 cm, find the length of PT.
4 marksHardStructured
Answer available
Class 10 · Mathematics · Circles
State the angle in a semicircle theorem.
2 marksEasyShort answer
Answer available
Class 10 · Mathematics · Circles
The angle between a tangent to a circle and the radius drawn to the point of contact is:
1 markMediumMCQ
Answer available
Class 10 · Mathematics · Circles
In a circle with centre O, the angle AOB at the centre is 100°. Find the angle ACB at a point C on the major arc.
2 marksEasyNumerical
Answer available
Class 10 · Mathematics · Circles
Assertion: a parallelogram inscribed in a circle must be a rectangle. Reason: the opposite angles of a cyclic quadrilateral are supplementary. State whether both are true and whether the reason explains the assertion.
2 marksMediumAssertion–reason
Answer available
Class 10 · Mathematics · Circles
In a circle with centre O, an arc subtends an angle of 110° at the centre. Find the angle subtended by the same arc at a point on the remaining part of the circle.
2 marksEasyNumerical
Answer available
Class 10 · Mathematics · Circles
The opposite angles of a cyclic quadrilateral are:
1 markEasyMCQ
Answer available
Class 10 · Mathematics · Circles
PQ is a tangent at P to a circle with centre O. If OQ = 25 cm and the radius of the circle is 7 cm, find the length of PQ.
3 marksMediumStructured