SSC CGL Quant – Geometry – Tier II Level · Marathon

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SSC CGL Quant – Geometry – Tier II Level · Marathon – 12 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.  
Two circles of radii 6 cm and 2 cm have their centres 4 cm apart. How many common tangents can be drawn?

Correct Answer: B [1]

Explanation:

d = r₁ − r₂ → they touch internally → only 1 common tangent (at the point of contact).

2.  
In triangle ABC, AB = 7, AC = 9 and BC = 8. What is the length of the median AD?

Correct Answer: C [7]

Explanation:

Apollonius: 49 + 81 = 2(AD² + 16) → AD² = 49 → 7.

3.  
PT is a tangent at T and chord TA makes ∠ATP = 58° with it. C is a point on the minor arc TA. What is ∠TCA?

Correct Answer: D [122°]

Explanation:

Angle in the alternate (major) segment = 58°; C is in the other segment, so ∠TCA = 180° − 58° = 122°.

4.  
The interior angles of a regular polygon add up to 2340°. How many diagonals does it have?

Correct Answer: D [90]

Explanation:

(n − 2)180 = 2340 → n = 15 → 15 × 12/2 = 90.

5.  
Two circles of radii 5 cm and 3 cm have centres 17 cm apart. What is the length of a transverse common tangent?

Correct Answer: A [15 cm]

Explanation:

√(17² − (5 + 3)²) = √225 = 15 cm.

6.  
In triangle ABC, DE ∥ BC with AD : DB = 3 : 4. What is the ratio of the area of triangle ADE to the area of trapezium DBCE?

Correct Answer: C [9 : 40]

Explanation:

AD : AB = 3 : 7 → areas 9 : 49 → trapezium 49 − 9 = 40 → 9 : 40.

7.  
In a cyclic quadrilateral ABCD, ∠A − ∠C = 40°. What is ∠A?

Correct Answer: B [110°]

Explanation:

∠A + ∠C = 180 and ∠A − ∠C = 40 → ∠A = 110°.

8.  
Statement-basedWhich of the following is/are correct?
I. Each exterior angle of a regular hexagon is 60°.
II. The diagonals of every rhombus are equal.
III. The orthocentre of a right triangle is the vertex of the right angle.

Correct Answer: B [I and III only]

Explanation:

II is wrong (only a square's are equal).

9.  
What is the inradius of a right triangle with sides 10 cm, 24 cm and 26 cm?

Correct Answer: C [4 cm]

Explanation:

r = (a + b − c)/2 = (10 + 24 − 26)/2 = 4 cm (also Δ/s = 120/30).

10.  
Two secants from an external point P meet a circle at A, B and at C, D. PA = 3 cm, PB = 12 cm and PC = 4 cm. What is PD?

Correct Answer: D [9 cm]

Explanation:

PA × PB = PC × PD → 36 = 4 × PD → 9 cm.

11.  
The incircle of triangle ABC touches BC at D. AB = 9 cm, BC = 11 cm and CA = 8 cm. What is BD?

Correct Answer: A [6 cm]

Explanation:

s = (9 + 11 + 8)/2 = 14; the tangent length from B is s − CA = 14 − 8 = 6 cm.

12.  
Two circles of radii 10 cm and 17 cm intersect, and their centres are 21 cm apart. What is the length of the common chord?

Correct Answer: A [16 cm]

Explanation:

Distances from the centres: d₁ + d₂ = 21 and 100 − d₁² = 289 − d₂² → d₂ − d₁ = 9 → d₁ = 6.

➤ 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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