Geometry (Part-8)

Total Questions: 50

11. If the radius of a circle is 8 cm, then find the length of its largest chord. [SSC CHSL 07/08/2023 (2nd Shift)]

Correct Answer: (a) 16 cm
Solution:

Longest chord of the circle is its diameter.
So, length of longest chord = 2 × 8 = 16cm

12. In a square ABCD, E is a point inside the square such that ∆DEC is an equilateral triangle. If E is joined to vertices A and B of the square, what is the degree measure of ∠AEB? [SSC CHSL 07/08/2023 (2nd Shift)]

Correct Answer: (b) 150°
Solution:

13. At one end of a diameter PQ of a circle of radius 8 cm a tangent APB is drawn to the circle. Find the length of the chord RS, which is parallel to AB and at a distance of 12 cm from P. [SSC CHSL 07/08/2023 (3rd Shift)]

Correct Answer: (d) 8√3 cm
Solution:

14. The perpendicular distance from the centre of a circle to the chord is 20 cm. Calculate the chord's length in centimetres if the circle's diameter is 58 cm. [SSC CHSL 07/08/2023 (4th Shift)]

Correct Answer: (a) 42
Solution:

15. The diameter PQ of a circle with centre O is perpendicular to the chord RS. PQ intersects RS at T. If RS = 16 cm and QT = 4 cm, what is the length (in cm) of the diameter of the circle? [SSC CHSL 07/08/2023 (4th Shift)]

Correct Answer: (a) 20
Solution:

RT × TS = PT × TQ
8 × 8 = PT × 4 ⇒ PT = 16
Diameter = PT + TQ = 16 + 4 = 20cm

16. Half of the length of the chord of a circle is 12 cm and the perpendicular distance between the centre and the chord is 5 cm. The radius of the circle is: [SSC CHSL 08/08/2023 (1st Shift)]

Correct Answer: (b) 13 cm
Solution:

17. ∆LON and ∆LMN are two right-angled triangles with common hypotenuse LN such that ∆LON = 90º and ∆LMN = 90º. LN is the bisector of ∠OLM. If LN = 29 cm and ON = 20 cm, then what is the perimeter (in cm) of ∆LMN ? [SSC CHSL 08/08/2023 (3rd Shift)]

Correct Answer: (d) 70
Solution:

Pythagorean triplets :- (20, 21, 29)
So, perimeter of triangle = 20 + 21 + 29 = 70 cm

18. In ∆ABC, ∠A = 5x - 60º, ∠B = 2x + 40°, ∠C = 3x - 80º. find m ∠A. [SSC CHSL 08/08/2023 (3rd Shift)]

Correct Answer: (c) 80°
Solution:

19. If the two interior opposite angles of an exterior angle of a triangle are 35° and 65°, then the measurement of the exterior angle is: [SSC CHSL 08/08/2023 (4th Shift)]

Correct Answer: (c) 100°
Solution:

Exterior angle = sum of two opposite interior angle of triangle = 35º + 65º = 100º

20. In a triangle ABC, AP, the bisector of ∠A, is perpendicular to BC at point P. The measures of BP and PC are x and 3y, respectively. The measures of AB and AC are 4x and (5y + 21) , what is the value of (x + y)? [SSC CHSL 08/08/2023 (4th Shift)]

Correct Answer: (c) 12
Solution: