1. The ratio of the areas of two triangles with the common base is 6:5. Height of the larger triangle is 9 cm. Then find the corresponding height of the smaller triangle.
2. A vertical pole of a length 6m casts a shadow of 4m long on the ground. At the same time a tower casts a shadow 28m long. Find the height of the tower.
3. Triangle ABC has sides of length 5, 6 and 7 units while ∆ PQR has perimeter of 360 units. If ∆ ABC is similar to ∆ PQR then find the sides of ∆ PQR.
4. The corresponding altitudes of two similar triangles are 6 cm and 9 cm respectively. Find the ratio of their areas.
5. A ladder 10m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from the base of the wall.
6. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.
7. Find the side of a square whose diagonal is 16 √2 cm.
8. Find the length of a altitude of an equilateral triangle, each side measuring 'a' units.
9. Adjacent sides of a parallelogram are 11 cm and 17 cm. If the length of one of its diagonals is 26 cm. Find the length of the other.
10. If two circles touch externally then show that the distance between their centres is equal to the sum of their radii.
11. If two circles with radii 8 and 3 respectively touch internally then show that the distance between their centres is equal to the difference of their, find that distance.
12. Two circles which are not congruent touch externally. The sum of their areas is 130 π sq. cm. and the distance between their centres is 14 cm. Find radii of circles.
13. Find the radius of the circle passing through the vertices of a right angled triangle when lengths of perpendicular sides are 6 and 8.
14. If the chord AB of a circle is parallel to the tangent at C, then prove that AC = BC.
15. Let two circles intersect each other at points A and D. Let the diameter AB intersect the circle with centre P at point N and diameter AC intersect the circle in point M with centre Q. Then prove AC.AM = AB.AN.
16. Construct any right angled triangle and draw incircle of that triangle.
17. Construct the circumcircle and incircle of an equilateral ∆ XYZ with side 6.3 cm.
18. Draw a tangent at any point 'M' on the circle of radius 2.9 cm and centre 'O'.
19. Draw a tangent at any point R on the circle of radius 3.4 cm and centre 'P'.
20. Draw a circle having radius 3 cm. Draw a chord XY = 5cm. Draw tangents at point X and Y without using centre.
21. Construct ∆ LMN such that LM = 6.6 cm. ∠ LMN = 650 and ND is median and ND = 5 cm.
22. The terminal arm is in II quadrant, what are the possible angles?
23. The terminal arm is on negative Y - axis. What are the possible angles? What can you say about this angles?
24. Prove that: sec2θ + cosec2 θ = sec2θ × cosec2θ
25. x = a sec θ , y = b tanθ , then Eliminate θ
26. The angle of elevation of a cloud as seen from a point 400 meters above a lake is 300 and the angle of depression of its reflection in the lake is 450. Find the height of the cloud above the lake. (√3 = 1.73)
27. Find the value of k if ( - 3, 11), (6 , 2) and ( k , 4) are collinear points.
28. If (4 , - 3 ) is a point on the line 5x + 8 y = c, then find c.
29. Find the equation of the line passing through (2 , -1) and parallel to 3x + 4y = 10.
30. An arc of a circle having measure 360 has length 176m. Find the circumference of the circle.
31. Find the area of sector whose arc length and radius are 10cm and 5 cm respectively.
32. The perimeter of one face of a cube is 24 cm. Find the total surface of 6 faces and the volume of the cube.
33. The curved surface area of a cone is 4070 sq. cm. and its diameter is 70 cm. What is its slant height?
34. A cone of height 24 cm has a plane base of surface area 154 sq. cm. Find its volume.