Quant · Geometry

Geometry

4 sub-topics · 58 lessons · 76 questions · 26 PYQs

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Lines, Angles and Polygons11 lessons · 12 questions · 2 PYQs

Triangles19 lessons · 30 questions · 12 PYQs

Circles20 lessons · 25 questions · 10 PYQs

Quadrilaterals8 lessons · 9 questions · 2 PYQs

Formula sheet

Triangle inequality
$|b-c|<a<b+c$
Power of a point
$PA\cdot PB=PC\cdot PD=PT^2$
Diagonal triangles of a quadrilateral
$[AOB]\cdot[COD]=[AOD]\cdot[BOC]$
Length of a median (Apollonius)
$m_a=\frac{1}{2}\sqrt{2b^2+2c^2-a^2},\quad AG:GD=2:1$
Length of a chord
$\text{chord}=2\sqrt{r^2-d^2}$
Three formulas for the area of a triangle
$\text{Area}=\frac{1}{2}bh=\frac{1}{2}ab\sin C=\sqrt{s(s-a)(s-b)(s-c)}$
Number of diagonals of a polygon
$\text{diagonals}=\frac{n(n-3)}{2}=\binom{n}{2}-n$
Least area from two opposite triangles
$\text{min area}=\left(\sqrt{[AOB]}+\sqrt{[COD]}\right)^2$