SSC CGL Quant – Geometry – Level 3 · Challenge
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Half the difference of ∠B and ∠C: (70 − 40)/2 = 15°.
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SSC CGL Quant – Geometry – Level 3 · Challenge – 11 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.
Chords AB and CD intersect at P inside a circle. AP = 5, PB = 6 and CP = 3. What is PD?
Correct Answer: B [10]
Explanation:
AP × PB = CP × PD → 30 = 3 × PD → 10.
2.
From an external point P, a secant meets a circle at A and B (PA = 3 cm, AB = 9 cm) and a tangent touches it at T. What is PT?
Correct Answer: A [6 cm]
Explanation:
PB = 3 + 9 = 12; PT² = PA × PB = 3 × 12 = 36 → 6 cm.
3.
Two circles of radii 8 cm and 3 cm have their centres 13 cm apart. What is the length of a direct common tangent?
Correct Answer: C [12 cm]
Explanation:
√(13² − (8 − 3)²) = √144 = 12 cm.
4.
Odd one outWhich of these is NOT a Pythagorean triplet?
Correct Answer: B [(10, 24, 27)]
Explanation:
100 + 576 = 676 = 26², not 27².
5.
H is the orthocentre of an acute triangle ABC with ∠A = 70°. What is ∠BHC?
Correct Answer: D [110°]
Explanation:
∠BHC = 180° − ∠A = 110°.
6.
Data tablediagonals of polygons:
5 sides → 5 | 6 sides → 9 | 7 sides → 14
How many diagonals does a 12-sided polygon have?
5 sides → 5 | 6 sides → 9 | 7 sides → 14
How many diagonals does a 12-sided polygon have?
Correct Answer: A [54]
Explanation:
n(n − 3)/2 = 12 × 9/2 = 54.
7.
What is the circumradius of an equilateral triangle of side 12 cm?
Correct Answer: B [4√3 cm]
Explanation:
R = a/√3 = 12/√3 = 4√3 cm (inradius is half of it: 2√3).
8.
D and E are the midpoints of AB and AC of a triangle ABC whose perimeter is 30 cm. What is the perimeter of triangle ADE?
Correct Answer: A [15 cm]
Explanation:
Every side of ADE is half the corresponding side of ABC (midpoint theorem) → 15 cm.
9.
The bisectors of the exterior angles at B and C of triangle ABC meet at E. If ∠A = 64°, what is ∠BEC?
Correct Answer: C [58°]
Explanation:
Excentre: ∠BEC = 90° − ∠A/2 = 90 − 32 = 58° (the incentre would give 90 + 32 = 122°).
10.
In triangle ABC, ∠A = 70°. The bisector of ∠B and the bisector of the exterior angle at C meet at P. What is ∠BPC?
Correct Answer: D [35°]
Explanation:
∠BPC = ∠A/2 = 35°: the exterior angle at C is A + B, so half of it = half of B + ∠BPC.
11.
In triangle ABC, ∠B = 70° and ∠C = 40°. What is the angle between the altitude from A and the bisector of ∠A?
Correct Answer: A [15°]
Explanation:
Half the difference of ∠B and ∠C: (70 − 40)/2 = 15°.
➤ 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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