CBSE 10 Math Circles Practice Paper 07

CBSE 10 Mathematics Circles Practice Paper

1.  The lengths of tangents drawn from an external point to a circle are equal.

2. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

3. Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

4. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.

5. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

6. In Fig - 1, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X'Y' at B. Prove that ? AOB = 90°.

7. Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.

8. Prove that the parallelogram circumscribing a circle is a rhombus.

9. 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 and 6 cm respectively (see Fig - 2). Find the sides AB and AC.

10. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

11.  The tangent at any point of a circle is perpendicular to the radius through the point of contact.

12. Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠ PTQ = 2 ∠ OPQ.

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