81)

If the angle between the internal bisectors of two angles ∠B and ∠C of a triangle ABC is 125°, then the value of ∠A is:

SSC CHSL 2021

A)

62°

B)

65°

C)

70°

D)

72°

82)

Points D, E and F are on the sides AB, BC and AC, respectively, of triangle ABC such that AE, BF and CD bisect ∠A, ∠B and ∠C, respectively. If AB = 6 cm, BC = 7 cm and AC = 8 cm, then what will be the length of BE?

SSC CHSL 2021

A)

3.5 cm

B)

3.6 cm

C)

4 cm

D)

3 cm

83)

The perimeter of a right-angled triangle whose sides that make right angles are 15 cm and 20 cm is:

SSC CHSL 2021

A)

40 cm

B)

70 cm

C)

60 cm

D)

50 cm

84)

In ΔABC, D and E are the points on the sides AB and AC, respectively such that ∠AED = ∠ABC. If AE = 6 cm, BD = 2 cm, DE = 3 cm and BC = 5 cm, then (AB + AC) is equal to:

SSC CHSL 2021

A)

\(\frac{86}{3}\) cm

B)

\(\frac{70}{3}\) cm

C)

\(\frac{50}{3}\) cm

D)

\(\frac{49}{3}\) cm

85)

A circle is inscribed in a right-angled triangle. The lengths of the two sides containing the right angle are 15 cm and 8 cm. What is the radius of the in-circle?

SSC CHSL 2021

A)

4 cm

B)

3 cm

C)

4.5 cm

D)

3.75 cm

86)

If the perimeter of an isosceles right triangle is 15(√2 + 1) cm, then the area of the triangle will be:

SSC CHSL 2021

A)

55 cm²

B)

45 cm²

C)

46.5 cm²

D)

56.25 cm²

87)

The perimeter of an isosceles triangle is 220 cm. If the base is 40 cm, then the length of each of the other sides is:

SSC CHSL 2021

A)

80 cm

B)

85 cm

C)

95 cm

D)

90 cm

88)

The difference between the two perpendicular sides of a right-angles triangle is 17 cm and its area is 84cm². What is the perimeter (in cm) of the triangle?

SSC CHSL 2021

A)

65

B)

49

C)

72

D)

56

89)

Let O be the centre of a circle and AC be the diameter. BD is a chord intersecting AC at E. AD and AB are joined. If ∠BOC = 40° and ∠AOD = 120°, then ∠BEC is equal to

SSC CHSL 2021

A)

70°

B)

80°

C)

90°

D)

55°

90)

In a circle with center O, PA and PB are tangents to the circle at A and B, respectively, from an external point P. If, ∠AOB = 116° then what is the measure of ∠OPB?

SSC CHSL 2021

A)

32°

B)

90°

C)

30°

D)

58°