SSC CGL Quant – Geometry – Level 2 · Exam Level · Tier I Sprint

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SSC CGL Quant – Geometry – Level 2 · Exam Level · Tier I Sprint – 15 questions, subject: Quantitative Aptitude. Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.

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1.  
Diagram-basedO is the centre. Chord AB is 24 cm long and 5 cm from O. What is the radius?

Correct Answer: A [13 cm]

Explanation:

√(12² + 5²) = 13 cm.

2.  
A point is 17 cm from the centre of a circle of radius 8 cm. What is the length of the tangent from the point?

Correct Answer: B [15 cm]

Explanation:

√(17² − 8²) = √225 = 15 cm.

3.  
Diagram-basedPA and PB are tangents and O is the centre. What is ∠AOB?

Correct Answer: D [130°]

Explanation:

∠APB + ∠AOB = 180° (OAPB has two right angles) → 130°.

4.  
Diagram-basedABCD is a cyclic quadrilateral. Find x.

Correct Answer: C [70°]

Explanation:

Opposite angles of a cyclic quadrilateral add to 180° → 70°.

5.  
Diagram-basedIn the figure DE ∥ BC. What is EC?

Correct Answer: B [7.5]

Explanation:

AD/DB = AE/EC → 3/5 = 4.5/EC → EC = 7.5.

6.  
Two similar triangles have corresponding sides in the ratio 3 : 5. The smaller has area 27 cm². What is the area of the larger?

Correct Answer: D [75 cm²]

Explanation:

Areas ∝ squares of sides: 27 × 25/9 = 75 cm².

7.  
Diagram-basedI is the incentre of triangle ABC. What is ∠BIC?

Correct Answer: A [128°]

Explanation:

∠BIC = 90° + ∠A/2 = 90 + 38 = 128°.

8.  
O is the circumcentre of an acute triangle ABC with ∠A = 48°. What is ∠BOC?

Correct Answer: C [96°]

Explanation:

∠BOC = 2∠A = 96°.

9.  
Two-quantity comparison
Quantity I: each exterior angle of a regular pentagon
Quantity II: each interior angle of an equilateral triangle

Correct Answer: A [Quantity I > Quantity II]

Explanation:

QI = 360/5 = 72°; QII = 60°.

10.  
Trick SpotterTwo circles of radii 10 cm and 3 cm have centres 25 cm apart. Which is the fastest correct route to the direct common tangent?

Correct Answer: A [√(25² − (10 − 3)²)]

Explanation:

Direct → difference of radii: √(625 − 49) = 24 cm.

11.  
Spot My Mistake“∠BOC = 140° at the centre, so ∠BAC = 2 × 140° = 280°.” What is the correct ∠BAC (A on the major arc)?

Correct Answer: C [70°]

Explanation:

The angle at the circumference is HALF the central angle: 70°.

12.  
In triangle ABC, AB = 12, AC = 8 and BC = 15. The bisector of ∠A meets BC at D. What is BD?

Correct Answer: D [9]

Explanation:

BD : DC = 12 : 8 = 3 : 2 → BD = 15 × 3/5 = 9.

13.  
Assertion–Reason
A: The perpendicular from the centre of a circle to a chord bisects the chord.
R: The two right triangles formed are congruent by RHS (common side, equal radii).

Correct Answer: B [Both A and R are true and R explains A]

Explanation:

OM common, OA = OB, right angles at M → congruent → AM = MB.

14.  
Reverse questioneach interior angle of a regular polygon is 162°. How many sides does it have?

Correct Answer: D [20]

Explanation:

Exterior = 18° → 360/18 = 20.

15.  
The diagonals of a rhombus are 10 cm and 24 cm. What is its perimeter?

Correct Answer: C [52 cm]

Explanation:

Side = √(5² + 12²) = 13 → 4 × 13 = 52 cm.

➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Quantitative Aptitude book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-quantitative-aptitude

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