31. What can be the maximum number of common tangent which can be drawn to two non-intersecting circles?
32. Astha cuts a triangle out of a cardboard and tries to balance the triangle horizontally at the tip of her finger. On what point will she be able to balance the shape for any kind of triangle?
33. In an isosceles triangle ABC with AB = AC and AD is perpendicular to BC. If AD = 6 cm and the perimeter of ΔABC is 36 cm, then the area of ΔABC is:
34. Two circles of radii 15 cm and 10 cm intersect each other and the length of their common chord is 16 cm. What is the distance (in cm) between their centres?
35. The lengths of two sides of a parallelogram are 3 cm and 10 cm. What is the sum of the squares of the diagonals of the parallelogram?
36. 
In the given figure, PQR is a triangle in which angle P : angle Q : angle R = 3 : 2 : 1, and PR is perpendicular to RS. What will be the measure of angle TRS?
In the given figure, PQR is a triangle in which angle P : angle Q : angle R = 3 : 2 : 1, and PR is perpendicular to RS. What will be the measure of angle TRS?
37. Two circles touch each other at point X. Two common tangents of the circles meet at point P and none of the tangents passes through X. These tangents touch the larger circle at points B and C. If the radius of the larger circles 15 cm and CP = 20 cm, then what is the radius (in cm) of the smaller circle?
38. XY and XZ are tangents to a circle. ST is another tangent to the circle at the point R on the circle which intersects XY and XZ at S and T respectively, If XY = 9 cm and TX = 15 cm, then RT is:
39. Each of the circles of equal radii with centres A and B pass through the centre of one another. They cut at C and D then ∠DBC is equal to?
40. In ΔABC, D is a point on BC such that ∠ADB = 2∠DAC, ∠BAC = 70° and ∠B = 56°. What is the measure of ∠ADC?
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