IIM CAT 2026 cheat sheet for Geometry! 📱 Practice 1 Lakh+ PYQs on ExamBhai.com! - Free Study Material

Geometry Chapter Summary: CAT 2026 Core Concepts & Formulas

Mastering Geometry for the IIM CAT requires a firm grasp of fundamental theorems, spatial relationships, and coordinate properties. Below is a structured breakdown of essential formulas and principles across key geometrical sub-domains.

1. Triangles & Polygons

For any triangle with sides \(a\), \(b\), and \(c\), the semi-perimeter is \(s = \frac{a + b + c}{2}\). The area can be computed using Heron's formula: \[Area = \sqrt{s(s-a)(s-b)(s-c)}\]

• Inradius (\(r\)): \(r = \frac{Area}{s}\)
• Circumradius (\(R\)): \(R = \frac{abc}{4 \cdot Area}\)
• Sum of Interior Angles: For an \(n\)-sided polygon, \(Sum = (n - 2) \times 180^\circ\)
• Number of Diagonals: \(D = \frac{n(n - 3)}{2}\)

2. Circles & Tangents

Key properties governing circle geometry include chord theorems, secants, and tangent lengths.

• Intersecting Chords Theorem: If chords \(AB\) and \(CD\) intersect at point \(P\), then \(PA \times PB = PC \times PD\).
• Direct Common Tangent (DCT): \(DCT = \sqrt{d^2 - (r_1 - r_2)^2}\), where \(d\) is the distance between centers.
• Transverse Common Tangent (TCT): \(TCT = \sqrt{d^2 - (r_1 + r_2)^2}\)

3. Coordinate Geometry & Mensuration

Coordinate relationships and 3D mensuration yield high-yield questions in Quantitative Aptitude.

• Distance Formula: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
• Volume of a Cone: \(V = \frac{1}{3}\pi r^2 h\)
• Volume of a Frustum: \(V = \frac{1}{3}\pi h (R^2 + r^2 + R \cdot r)\)

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