Geometry is high-weightage but predictable. Master these 12 theorems and you'll solve most SSC geometry questions in under 30 seconds.
Geometry is formula + theorem driven — once you know the rule, questions are 30-second jobs. SSC repeats the same theorem patterns across years.
1. Pythagoras: a² + b² = c² (right triangle). Use for any "find the length" question. 2. Similar triangle ratio: if two triangles are similar, sides / medians / altitudes are in the same ratio. 3. Mid-point theorem: the segment joining midpoints of two sides is parallel to the third side and half its length. 4. Area ratio: for similar triangles, area ratio = (side ratio)².
5. Tangent-radius: a tangent is perpendicular to the radius at the point of contact. 6. Two tangents from external point: equal in length, and the line joining them bisects the angle. 7. Angle in semicircle: always 90°. 8. Inscribed angle theorem: inscribed angle = half the central angle subtending the same arc. 9. Chord properties: equal chords are equidistant from the centre; perpendicular from centre bisects the chord.
10. Parallelogram: opposite sides equal, opposite angles equal, diagonals bisect each other. 11. Trapezium area: (1/2) × (sum of parallel sides) × height. 12. Rhombus diagonals: bisect at 90°; area = (1/2) × d1 × d2.
Circle + tangent + triangle (similar triangle ratio) Triangle + median + centroid (centroid divides median 2:1) Quadrilateral + diagonal + area
Draw each theorem on a flashcard. Practise by drawing from memory — the visual is more retrievable than the verbal formula.
Find length of tangent from external point Find angle in a cyclic quadrilateral Find area of an inscribed triangle
SSCIntel's Quant practice serves these patterns with PYQ + Brutal difficulty.
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