71)

LetΔABC ~ΔRPQ and \(\frac {ar (\Delta ABC)}{ar(\Delta RPQ)} = \frac 4 9 \). If AB = 3 cm, BC = 4 cm and AC = 5 cm, then PQ (in cm) is equal to:

SSC CPO 2020

A)

12

B)

6

C)

5

D)

4.5

72)

In ΔABC,∠A = 66°.  AB and AC are produced to points D and E, respectively. If the bisectors of angle CBD and angle BCE meet at the point O, then∠BOC is equal to:

SSC CPO 2020

A)

57°

B)

93°

C)

114°

D)

66°

73)

In ΔABC, AB and AC are produced to points D and E, respectively. If the bisectors of ∠CBD and ∠BCE meet at the point O, and ∠BOC = 57°, then ∠A is equal to:

SSC CPO 2020

A)

66°

B)

93°

C)

114°

D)

57°

74)

Let Δ ABC ∼ Δ RPQ and \(\frac{{ar(\Delta ABC)}}{{ar(\Delta RPQ)}} = \frac{4}{9}\) . If AB = 3 cm, BC = 4 cm and AC = 5 cm, then RP (in cm) is equal to:

SSC CPO 2020

A)

4.5 cm

B)

12 cm

C)

5 cm

D)

6 cm

75)

The perimeter of a right triangle is 60 cm and its hypotenuse is 26 cm. What is the area (in cm²) of the triangle?

SSC CPO 2020

A)

96

B)

60

C)

120

D)

90

76)

In ΔABC, D is the median from A to BC. AB = 6 cm, AC = 8 cm, and BC = 10 cm. The length of median AD (in cm) is:

SSC CPO 2020

A)

3

B)

4.5

C)

5

D)

4

77)

In ΔABC, ∠A = 68°. If I is the incentre of the triangle, then the measure of ∠BIC is:

SSC CPO 2020

A)

124°

B)

68°

C)

54°

D)

148°

78)

In ΔABC, BD ⊥ AC at D, E is a point on BC such that ∠BEA = x°. If ∠EAC = 62° and ∠ EBD = 60°, then the value of x is:

SSC CPO 2020

A)

78°

B)

76°

C)

92°

D)

68°

79)

A circle is inscribed in a triangle ABC. It touches side AB, BC, and AC at points R, P, and Q respectively. If AQ = 2.6 cm, PC = 2.7 cm and BR = 3 cm, then the perimeter (in cm) of the triangle ABC is:

SSC CPO 2020

A)

33.2

B)

16.6

C)

28

D)

30

80)

In ΔABC, ∠A = 54°. If I is the incentre of the triangle, then the measure of ∠BIC is:

SSC CPO 2020

A)

68°

B)

54°

C)

117°

D)

148°