Please solve these questions in a book and check your answers next week. This is Assignment 1 of 2 in Circles for Class 9. You should take about 60 minutes to solve this assignment without taking any help or reference textual, human or web.
Question 1. Define the following and mark them in a circle: (I) Center of a circle (ii) Chord (iii) Secant (iv)
Sector (v) Major and Minor segment
Question 2. Complete the following statements.
(I) Equal chords of a circle subtend ___ .
(ii) If the angles subtended by the chords of a circle at the center are equal, then ___.
(iii) The perpendicular from the center of the circle to a chord ___.
(iv) The line drawn through the center of a circle to bisect a chord is ___.
Question 3. Find the length of a chord which is at a distance of 5cm from the centre of the circle whose radius is 10cm.
Question 4. AB and CD are two parallel chords of a circle lying on opposite sides of the center. AB=10 cm, CD=24 cm. If the distance between AB and CD is 17cm, Find the radius of the circle.
Question 5. PQ and RS are two parallel chords of a circle whose center is O and radius is 10 cm. If PQ=16 cm and RS=12 cm, Find the distance between PQ and RS, if they lie (i) on the same side of the centre O, and (ii) on opposite sides of the centre O.
Question 6. Given an arc of a circle, show how to complete the circle.
Question 7. In the figure 9.1, if a diameter of a circle bisects each of the two chords of the circle, prove that the chords are parallel.
Question 8. In the figure 9.2, if two chords of a circle are equally inclined to the diameter through their point of intersection, prove that the chords are equal.
Question 9. In the figure 9.3, PQ and RQ are two chords equidistant from the center. Prove that the diameter passing through Q bisects <PQR and <PSR.
Question 10. In fig 9.4, AB and AC are two equal chords of a circle whose center is O. If OD║AB and OE ║AC. prove that triangle ADE is an isosceles triangle.
