Chapter-wise questions

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1 hapter-wise questions ircles 1. In the given figure, is circumscribing a circle. ind the length of. 3 15cm 5 2. In the given figure, is the center and. ind the radius of the circle if = 18 cm and = 3cm 3. and are two parallel chords of a circle. If = 24cm & = 18cm and distance between these chords is 21cm find the radius of the circle. 4. The radii of two concentric circles are 15cm and 41cm. The chord of larger circle cuts the smaller circle at and. ind the length of if = 24cm. 5. In the given figure and are two tangents. ind if = 49º 6. rom a point outside the circle with radius 8 cm the distance to the centre of the circle is 17cm. ind the the length of the tangent.

2 hapter-wise questions 7. Two concentric circles are of radii 6cm and 10 cm. ind the length of the chord of the larger circle which touches the smaller circle 8. In the figure and are tangents from external point. is a third tangent, 5cm touching the circle at. If = 17cm and = 5cm find. 9. In the figure is a chord of the large circle which touches the small circle at. = 8cm and radius of the small circle is 3cm find the diameter of the large circle. 10. In the figure = 84º. find. 11. In the given figure, two circles touch each other externally at. rove that the common tangent at bisects the other two common tangents. 12. In the given figure, a circle is inscribed L H in a quadrilateral in which = 90º. If = 23cm, = 29cm and = 5cm, find the radius of the circle. 13. point is 13cm from the center of the circle. The length of the tangents drawn from to the circle is 12cm. ind the radius of the circle. 14. In the given figure, X and X are tangents from to the circle with center. is a point on the circle. rove that X + = X +. X 15. how that the tangent lines drawn at the end points of the diameter of a circle are parallel.

3 hapter-wise questions 16. circle is inscribed in a triangle having sides 8cm, 10 cm and 12cm as shown in the figure. ind, and. 17. If,, are tangents in the given figure, X and = 5cm. ind the perimeter of. 18. In the given figure, is a right triangle right angled at such that = 6cm and = 8cm. ind the radius of its incircle. 19. In the given figure l and m are two parallel tangents at and. The tangent at makes an intercept between l and m. rove that = 90º l m 20. circle is touching the side of at and touching and produced at and respectively. rove that = 1 (erimeter of ) In the given figure, T = 6cm = 5cm. ind the length of. 6 cm T 5 cm rove that the lengths of the tangents drawn from an external point to a circle are equal. Using the above theorem, prove that: If quadrilateral is circumscribing a circle, then + = rove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. Using the above, do the following: In the figure below, is the centre of the two concentric circles. is a chord of the larger circle touching the smaller circle at. rove that =.

4 hapter-wise questions 24. In the given figure = and = 20 find the measure of In the figure chords and of the circle intersect at 0. = 5cm, = 3cm, and = 2.5 cm. etermine length of. 26. rove that the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. Using the above, do the follwing rove that the angle formed by a chord in the major segment is acute. 27. rove that the sum of either pair of opposite angles of a cyclic quadrilateral is 180. Using the above, do the following: In figure 3, is a cyclic quadrilateral in which = (x+y+10), = (y+20), = (x+y 30) and = (x+y). ind x and y. igure In the given figure, is diameter of a circle with centre. If = 65, = 40, M = 50, find, and M M

5 hapter-wise questions 29. The sum of either pair of opposite angles of a cyclic quadrilateral is 180. rove Using the above result, in figure 2. is a cyclic quadrialteral. circle passing through and meets and in the points and respectively. rove that

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