SSC Advanced Maths Formulas & Theorems
1. Geometry (Triangles & Circles)
- Inradius of Right-Angled Triangle: $r = \frac{a + b - c}{2}$
- Circumradius of Right-Angled Triangle: $R = \frac{c}{2}$ (Half of Hypotenuse)
- Centroid Theorem: Centroid divides each median in ratio $2:1$.
- Tangent-Secant Theorem: If $PT$ is tangent from external point $P$ and $PAB$ is secant, then $PT^2 = PA \times PB$.
2. Algebra Shortcuts
- If $x + \frac{1}{x} = k$, then:
- $x^2 + \frac{1}{x^2} = k^2 - 2$
- $x^3 + \frac{1}{x^3} = k^3 - 3k$
- If $x + \frac{1}{x} = \sqrt{3}$, then $x^6 = -1$ and $x^6 + 1 = 0$.
- If $a + b + c = 0$, then $a^3 + b^3 + c^3 = 3abc$.