61)

In ∆ ABC, ∠B = 90⁰, AB = 8 cm and BC = 15 cm, D is a point on BC such that AD bisects ∠A. The length (in cm) of BD is:

SSC CHSL 2021

A)

4.5

B)

3.6

C)

4.2

D)

4.8

62)

How many isosceles triangles with integer sides are possible such that the sum of two of the sides is 16 cm?

SSC CHSL 2021

A)

15

B)

24

C)

9

D)

18

63)

The side BC of a triangle ABC is extended to a point D. If ∠ACD = 117° and ∠ABC = \frac{5}{8} ∠BAC. then what is the measure of ∠ABC ?

SSC CHSL 2021

A)

36°

B)

54°

C)

72°

D)

45°

64)

The sides AB and AC of a ∆ABC are produced up to points D and E. The bisectors of the exterior angles to formed. intersect each other at point I if ∠ACB is 66⁰ and ∠ABC is 44, then what is the measure (in degrees) of ∠BIC?

SSC CHSL 2021

A)

52

B)

50

C)

55

D)

48

65)

The side BC of \(\triangle ABC\) is produced to D. The bisectors of ∠ ABC  and ∠ ACD meet at E. If AB = AC and ∠ BEC = 35°, then the measures of ∠ABC will be:

SSC CHSL 2021

A)

75°

B)

35°

C)

55°

D)

45°

66)

In \( \triangle ABC\), ∠B = 90° . AD and CE are the medians drawn from A and C, respectively. If AC = 10 cm and AD =√ 55 cm, then the length of CE is:

SSC CHSL 2021

A)

√ 70 cm

B)

5√ 3 cm

C)

√ 66 cm

D)

2√ 15 cm

67)

ΔABC is right-angled at B and D is a point on AC such that BD is perpendicular to AC. If BD = 6 cm and AD = 3 cm, then what will be the length of AC?

SSC CHSL 2021

A)

9 cm

B)

12 cm

C)

15 cm

D)

18 cm

68)

In Δ ABC, DE || BC, where D and E are points on the sides AB and AC, respectively. If AD = 2 cm, BD = 5.2 cm, AC = 9 cm and AE = x cm, then what is the value of x?

SSC CHSL 2021

A)

2.5

B)

4

C)

3

D)

3.5

69)

ΔPQR is inscribed in a circle. The bisector of ∠P cuts QR at S and the circle at T .If PR = 5 cm,  PS = 6 cm and ST = 4 cm, then the length (in cm ) of PQ is:

SSC CHSL 2021

A)

13

B)

15

C)

12

D)

10

70)

In ΔABC, D and E are points on sides AB and BC, respectively, such that BD ∶ DA = 1 ∶ 2 and CE ∶ EB = 1 ∶ 4, If DC and AE intersect at F, then FD ∶ FC is equal to:

SSC CHSL 2021

A)

3 ∶ 2

B)

4 ∶ 1

C)

5 ∶ 2

D)

8 ∶ 3