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Quantitative Aptitude›Ch 4: Algebra, Geometry & Mensuration›Circles and Quadrilaterals
Mastering chords, tangents, and polygon properties for competitive exams.
A tangent is always perpendicular to the radius at the point of contact. In a cyclic quadrilateral, the sum of opposite angles is always 180 degrees.
Memory Shortcuts
| Shape Name | Sides (n) | Total Sum |
|---|---|---|
| Triangle | 3 | 180° |
| Quadrilateral | 4 | 360° |
| Pentagon | 5 | 540° |
| Hexagon | 6 | 720° |
Tangent
(Contact point 90°)
Contact point 90°
Radius and tangent meet at right angles.
Cyclic Quad
(Vertex on Circle)
Vertex on Circle
Opposite angles sum is 180 degrees.
Rhombus
(Equal Sides)
Equal Sides
Diagonals cut each other at 90 degrees.
Chord
(Line in Circle)
Line in Circle
Perpendicular from center bisects the chord.
Parallelogram diagonals are equalOnly equal in Rectangle/Square
General parallelogram diagonals only bisect each other, they are not equal in length.
Exterior angle sum depends on nSum is always 360 degrees
For any convex polygon, the sum of all exterior angles is always 360°, regardless of the number of sides.
Every rhombus is a squareOnly if angles are 90 degrees
A rhombus only guarantees equal sides. To be a square, it must also have 90 degree angles.
Q1.What is the measure of each interior angle of a regular hexagon?
Q2.In a cyclic quadrilateral ABCD, if angle A = 80°, what is the value of angle C?