121)

In triangle ABC, the bisector of angle BAC meets BC at point D in such a way that AB = 10 cm, AC = 15 cm and BD = 6 cm. Find the length of BC (in cm).

SSC CGL 2022

A)

17

B)

11

C)

15

D)

9

122)

In a triangle ABC, points P and Q are AB and AC, respectively, such that AP = 4 cm, PB = 6 cm, AQ = 5 cm and QC = 7.5 cm. If PQ = 6 cm, then find BC (in cm).

SSC CGL 2022

A)

10

B)

9

C)

15

D)

12

123)

In the following figure, AD bisects angle BAC. Find the length (in cm) of BD.

SSC CGL 2022

A)

5

B)

9

C)

4

D)

6

124)

In ∆ABC, the perpendiculars drawn from A, B and C meet the opposite sides at points D, E and F, respectively. AD, BE and CF intersect at point P. If ∠EPD = 110° and the bisectors of ∠A and ∠B meet at point Q, then ∠AQB = ?

SSC CGL 2022

A)

125°

B)

135°

C)

110°

D)

115°

125)

In a right-angled triangle PQR, right-angled at Q, the length of the side PR is 17 units, length of the base QR is 8 units, and length of the side PQ is 15 units. If ∠RPQ = α, then sin α + cos α is:

SSC CGL 2022

A)

\(\frac{21}{17}\)

B)

\(\frac{23}{17}\)

C)

\(\frac{18}{17}\)

D)

\(\frac{15}{17}\)

126)

In the triangle ABC, AB = 12 cm and AC = 10 cm, and ∠BAC = 60°. What is the value of the length of the side BC?

SSC CGL 2022

A)

13.20 cm

B)

7.13 cm

C)

10 cm

D)

11.13 cm

127)

If areas of similar triangles ΔABC and ΔDEF are x² cm² and y² cm² respectively, and EF = a cm, then BC (in cm) is:

SSC CGL 2022

A)

\(\frac{a x}{y}\)

B)

\(\frac{y}{a x}\)

C)

\(\frac{y^2}{a^2 x^2}\)

D)

\(\frac{a^2 x^2}{y^2}\)

128)

The side of an equilateral triangle is 12 cm. What is the radius of the circle circumscribing this equilateral triangle?

SSC CGL 2022

A)

9√3 cm

B)

4√3 cm

C)

6√3 cm

D)

5√3 cm

129)

If the angles of a triangle are (x - 46) degrees, (x + 96) degrees and 8x degrees, then what is the value of 2x?

SSC CGL 2022

A)

26 degrees

B)

24 degrees

C)

15 degrees

D)

13 degrees

130)

If the figure, AB = AD = 7 cm and AC = AE and BC = 11 cm, then find the length of ED.

SSC CGL 2022

A)

11

B)

10

C)

12

D)

2