Sample Paper – 2010
Class – X
Subject - Mathematics
1 | A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12 cm. Find the radius of the circle. | 5 cm |
2 | In figure if AB=AC, prove that BE=EC.
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3 | In fig. AQ and AR are tangents from A to the circle with centre O. P is a point on the circle. Prove that AB+BP=AC+CP |
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4 | In fig. ABC is a right-angled at B such that BC=6 cm and AB=8 cm. Find the radius of its incircle. |
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5 | Two concentric circles have radii 5 cm and 3 cm . Find the length of the chord of the larger circle which touches the smaller circle. |
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6 | Prove that the segment joining the points of contact of two parallel tangents passes through the centre. |
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7 | If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus. |
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8 | A circle is touching the side BC of |
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BRCM PUBLIC SCHOOL,BAHAL
PRACTICE SET - 3
Circles
9 | Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that |
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10 | A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm an 6 cm respectively. Find the sides AB and AC. |
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11 | Prove that, the tangent at any point of a circle is perpendicular to the radius through point of contact. |
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12 | Prove that, the length of tangents drawn from external point to circle is equal. |
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13. | The in circle of |
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14. | Prove that the tangents at the extremities of any chord make equal angles with the chord. |
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15. |
| AD=7 cm BE = 5 cm CF = 3 cm |
16. | Show that tangent lines at the end points of a diameter of a circle are parallel. |
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17. |
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18. | A circle touches the sides of a quadrilateral ABCD at P, Q, R, S respectively. Show that the angles subtended at the center by a pair of opposite sides are supplementary. |
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