Geometry

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41 ABC is a right-angled triangle with AB = 6 cm and BC = 8 cm. A circle with center O has been inscribed inside ΔABC. The radius of the circle is

A
1 cm
B
2 cm
C
3 cm
D
4 cm

42 A trapezoid A, B, C, D, and E has bases of length 10 and 14 cm. If the height of the trapezoid above is 5 unit's, what is the length of the diagonal BC? 

A
13
B
10
C
12
D
14

43 In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is :

A
6
B
8
C
10
D
12

44 Given a triangle ABC, another triangle is formed by connecting the midpoints of the sides of the triangle ABC, then the area of the new triangle formed will be how many times the area of the triangle ABC 

A
One fourth
B
Half of
C
One third of
D
Cannot be determined

45 In a right angled triangle ΔDEF, if the length of the hypotenuse EF is 12 cm, then the length of the median DX is:

A
3 cm
B
4 cm
C
6 cm
D
12 cm

46 The difference b/w two parallel sides of a trapezium is 8 cm and the perpendicular distance b/w them is 38 cm. Find the lengths of the parallel sides, if the area of the trapezium is 950 cm 2 :

A
32 and 28 
B
 29 and 21
C
16 and 24
D
32 and 18

47 Find the 25 % of sum of all the exterior angles of a cylic quadrilateral:

A
180
B
360
C
90
D
120

48 Let O be the in-centre of a triangle ABC and D be a point on the side BC of ΔABC, such that OD ⊥ BC. If ∠BOD = 15°, then ∠ABC = ?

A
75°
B
45°
C
150°
D
90°

49 If the length of the sides of a triangle are in the ratio 4 : 5 : 6 and the inradius of the triangle is 3 cm, then the altitude of the triangle corresponding to the largest side as base is :

A
7.5 cm
B
6 cm
C
10 cm
D
8 cm

50 In a right-angle ΔABC, ∠ABC = 90°, AB = 5 cm and BC = 12 cm. The radius of the circumcircle of the triangle ABC is:

A
7.5 cm
B
6 cm
C
6.5 cm
D
7 cm