### Section A

1. Sides of two similar triangles are in the ratio 4:9. Areas of these triangles are in the ratio. 1 Mark
(a) 2:3.
(b) 4:9
(c) 81:16
(d) 16:81

2.number of tangents to a circle which are parallel to a secant is or are:                                   1 Mark

(A)  1                      (B) 0                         (C) 2                                   (D) infinity many

3. What do you say about the line which is perpendicular to the radius of the circle through the point of contact?                                                                                                                                  1 Mark

4.If D and E are points on the respective sides AB and AC of ABC such that AD = 6 cm,
BD = 9 cm, AE = 8cm, EC = 12cm. Prove that DE || BC.                                                          1 Mark

### Section B

5.If two poles 5 m and 15 m high are 100 m apart, then find the height of the point of  intersection of the line joining the top of each pole to the foot of the opposite pole.                                          2 Marks

6.If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then find the length of each tangent.                                                                                                                               2 marks

7.ABC is an isosceles triangle right angled at C. Prove that ABsquare = 2 AC square.            2 marks

8. find mode of the following:

Marks :   0-10    10-20     20-30.    30-40.    40-50

Number of students:  3.   12     32     20       6                                                                              2 marks

### Section C

9.A chord AB of a circle of radius 10cm makes a right angle at the centre of the circle. Find the area of the major and minor segments.                                                                                           3 marks

10.In figure ABCD is a rectangle with AB =14 cm and BC =7 cm. Taking DC, BC and AD as
diameter, three semicircles are drawn. Find the area of the shaded portion.                           3 marks

11.Prove that the parallelogram circumscribing a circle is a rhombus.                                   3 marks

12. 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 angle AOB =90°.                     3 marks

### Section D

13. If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.                                                                                                4 Marks. .

14.If a hexagon ABCDEF circumscribe a circle, prove that AB + CD + EF = BC + DE + FA.  4 marks

15. Draw a pair of tangent to a circle of radius 5 cm which are inclined to each other at an angle  of 60°.                                                                                                                                           4 Marks

16.Find the mean of the following frequency distribution:                                 4 Marks

Classes:        0-20  20-40 40-60  60-80   80-100

Frequency:   15        18        21        29      17