Geometry Formulas for SSC CGL
Most geometry questions are one formula plus one step.
SSC CGL geometry covers what the syllabus calls "elementary geometric figures and facts": triangles and their centres, congruence and similarity, circles, chords, tangents and common tangents, and polygons. Mensuration, the area and volume of shapes, sits right next to it.
Most geometry questions are one formula plus one step. Below are the formulas grouped by figure, then worked practice questions that show each one in use.
You save ₹450
- Full-length Tier 1 & Tier 2 mocks
- Section-wise speed drills
- General Awareness question bank
One payment, no subscription
Triangle and Polygon Formulas
| Topic | Formula or fact |
|---|---|
| Pythagoras (right triangle) | hypotenuse² = base² + height² |
| Centroid (where medians meet) | Divides each median in the ratio 2 : 1 from the vertex |
| Incentre I (where angle bisectors meet) | ∠BIC = 90° + ∠A/2 |
| Circumcentre O (where perpendicular bisectors meet) | ∠BOC = 2∠A, when ∠A is acute |
| Orthocentre H (where altitudes meet) | ∠BHC = 180° − ∠A, in an acute triangle |
| Similar triangles | Ratio of areas = square of ratio of corresponding sides |
| Equilateral triangle, side a | Height = (√3/2)a; area = (√3/4)a²; inradius = a/(2√3); circumradius = a/√3 |
| Polygon with n sides | Sum of interior angles = (n − 2) × 180° |
| Regular polygon with n sides | Each exterior angle = 360°/n |
Circle Formulas
| Topic | Formula or fact |
|---|---|
| Angle at centre | Twice the angle at the circumference on the same arc |
| Angle in a semicircle | 90° |
| Perpendicular from centre to a chord | Bisects the chord |
| Tangent and radius | Meet at 90° at the point of contact |
| Tangent length from a point at distance d | √(d² − r²) |
| Two tangents from one outside point | Equal in length |
| Cyclic quadrilateral | Opposite angles add to 180° |
| Direct common tangent, radii r₁ and r₂, centres d apart | √(d² − (r₁ − r₂)²) |
| Transverse common tangent | √(d² − (r₁ + r₂)²) |
Mensuration Formulas
r = radius, h = height, l = slant height, s = half the perimeter.
Triangle with sides a, b, c (Heron)
Area or surface
√(s(s − a)(s − b)(s − c))
Volume
-
Circle
Area or surface
Area πr²; circumference 2πr
Volume
-
Cylinder
Area or surface
Curved surface 2πrh
Volume
πr²h
Cone
Area or surface
Curved surface πrl
Volume
(1/3)πr²h
Sphere
Area or surface
4πr²
Volume
(4/3)πr³
Hemisphere
Area or surface
Total surface 3πr²
Volume
(2/3)πr³
| Shape | Area or surface | Volume |
|---|---|---|
| Triangle with sides a, b, c (Heron) | √(s(s − a)(s − b)(s − c)) | - |
| Circle | Area πr²; circumference 2πr | - |
| Cylinder | Curved surface 2πrh | πr²h |
| Cone | Curved surface πrl | (1/3)πr²h |
| Sphere | 4πr² | (4/3)πr³ |
| Hemisphere | Total surface 3πr² | (2/3)πr³ |
Data interpretation and arithmetic in the exam style. No signup.
Worked Practice Questions
Original practice questions, not taken from any past paper.
- 1
Practice question 1: In triangle ABC, ∠A = 70° and I is the incentre. Find ∠BIC.
∠BIC = 90° + 70°/2 = 90° + 35° = 125°.
- 2
Practice question 2: In an acute triangle ABC, ∠A = 50° and O is the circumcentre. Find ∠BOC.
∠BOC = 2 × 50° = 100°. The angle at the centre is twice the angle at the circumference.
- 3
Practice question 3: Two circles of radii 8 cm and 3 cm have centres 13 cm apart. Find the lengths of the direct and transverse common tangents.
Direct: √(13² − (8 − 3)²) = √(169 − 25) = √144 = 12 cm. Transverse: √(13² − (8 + 3)²) = √(169 − 121) = √48 = 4√3 cm.
- 4
Practice question 4: Each interior angle of a regular polygon is 140°. How many sides does it have?
Each exterior angle = 180° − 140° = 40°. Number of sides = 360° ÷ 40° = 9.
- 5
Practice question 5: Two similar triangles have corresponding sides in the ratio 3 : 5. Find the ratio of their areas.
Square the side ratio: 3² : 5² = 9 : 25.
- 6
Practice question 6: An equilateral triangle has side 12 cm. Find its height, inradius and circumradius.
Height = (√3/2) × 12 = 6√3 cm. Inradius = 12/(2√3) = 2√3 cm. Circumradius = 12/√3 = 4√3 cm. Check: circumradius is twice the inradius, and the two add up to the height.
- 7
Practice question 7: A point is 13 cm from the centre of a circle of radius 5 cm. Find the length of the tangent from the point.
√(13² − 5²) = √(169 − 25) = √144 = 12 cm.
- 8
Practice question 8: Find the area of a triangle with sides 13, 14 and 15 cm.
s = (13 + 14 + 15) ÷ 2 = 21. Area = √(21 × 8 × 7 × 6) = √7056 = 84 cm².
How SSC Tests Geometry, and the Traps
Geometry questions usually name a figure and one or two measurements, then ask for an angle or a length. The skill being tested is choosing the right formula fast. A rough sketch, even a tiny one, stops most mistakes.
The common traps: mixing up the incentre (90° + A/2) and circumcentre (2A) formulas; using r₁ + r₂ for the direct common tangent when it needs r₁ − r₂; and squaring the side ratio for perimeters, which actually stay in the plain side ratio. Only areas use the square.
How to Make the Formulas Stick
- checkWrite the three tables from memory once a week until they come out complete
- checkLearn each formula with one quick example, like the ones above
- checkKeep the four triangle centres apart: centroid (medians), incentre (angle bisectors), circumcentre (perpendicular bisectors), orthocentre (altitudes)
- checkDraw the figure for every question, even in a timed set
- checkCheck answers with a known case, such as an equilateral triangle or the 3-4-5 triangle
FAQs
Which geometry topics are in the SSC CGL syllabus?expand_more
Triangles and their centres, congruence and similarity of triangles, circles with chords, tangents and the angles chords subtend, and common tangents to two or more circles. Mensuration of 2D and 3D shapes is listed separately.
What are the most important geometry formulas for SSC CGL?expand_more
The triangle centre angle formulas, the similar triangle area rule, polygon angle sums, the circle facts (angle at centre, tangent length, cyclic quadrilateral) and the two common tangent formulas. SSC publishes no weightage, so cover the full tables above.
How do I solve SSC geometry questions faster?expand_more
Know the formulas without looking them up, sketch the figure, and use special cases to check. Most questions need one formula and one step.
Next steps
Take a full SSC CGL mock testThe whole Tier 1 syllabus in one timed, scored paper.