Given below are the **Class 9 Maths** Assignments for Circles

b) Calculation problems

c) Multiple choice questions

d) Long answer questions

e) Fill in the blank's

Q1. If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, prove that the chords are equal.

Q2. If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angle with the chords.

Q3. If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D. Prove that AB = CD.

Q4. Three girls Reshma, Salma and Mandip are playing a game by standing a circle of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Salma and Mandip is 6 m each, what is the distance between Reshma and Mandip.

Q5. A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.

Q6. Prove that the quadrilateral formed (if possible) by the internal angle bisectors of any quadrilateral is cyclic.

Q7. If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that is a rectangle.

Q8. If the non- parallel sides of a trapezium are equal. Prove that its equal cyclic.

Q9. If circles are drawn taking two sides of a triangle as diameter, prove that the point of intersection of these circles on the third side.

Q10. ABC and ADC are two right triangles with common hypotenuse AC. Prove that <CAD = <CBD.

Q12. AB and CD are two chords of a circle such that AB = 6 cm, CD = 12 cm and AB 11 C of the distance between AB and CD is 3 cm, find the radius of circle.

Q13. Prove that the line joining the mid- points of two parallel chords of a circle passes through the centre.

Q14. Prove that a diameter of the circle which bisects a chord of the circle also bisects the angle subtended by the chord at centre of circle.

Q15. An equilateral triangle of side 9 cm is inscribed in the circle. Find the radius of the circle.

Q16. Prove that the perpendicular bisectors of sides of a cyclic quadrilateral are concurrent.

Q17. If two sides of pair of opposite sides of a cyclic quadrilateral are equal, prove that it diagonals are equal.

Q18. If the non- parallel sides of trapezium are equal, prove that it is cyclic.

Q19. Three scouts Rajat, Rohit and Ramit in the cultural show holded three stringed balloons with a message ‘Stop Child Labour’. Keeping themselves on boundary of a circle of radius 25 cm, each scout holded the string tightly. Find the distance between Rajat and Rohit, between Rohit and Ramit is 30 cm. What message was given by scouts and why?

Q20. Prove that the circle drawn with any one side of rhombus as diameter, passes through point of intersection of its diagonals.

Q21. A chord of a circle is equal to radius of circle. Find the angle subtended by chord at a point on mirror ad also at point on major arc.

Q22. Prove that the circle drawn on any one of equal sides of an isosceles ? as diameter bisects the base.

Q23. P, Q and R are three points on circle. Prove that perpendicular bisectors of PQ, QR and RP are concurrent.

Q24. PQ and PR are two equal chords of circle prove that the bisectors of angle QPR passes through centre of circle.

Q25. A circular park of radius 20 m is situated in a colony. Three friends Vishal, Naman and Deepak are sitting at equal distances on boundary each having a cell phone in its hand to talk to each other. Find the straight distance among them . Write the importance of communication?

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