Circle | Circle class 10 question

Mathematics Question for revision

There will be 10 questions and timing will be 1 hour.

1. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Find the Length of PQ.

2. In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to

3. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 80°, What is the value of ∠ POA ?

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

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

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

7. 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. 10.14). Find the sides AB and AC.

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

9.A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC

10.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.

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