Tangential Quadrilateral Formula

Posted In: Mathematics

In Euclidean geometry, a tangential quadrilateral (or tangent quadrilateral) or circumscribed quadrilateral is a convex quadrilateral whose sides are all tangent to a single circle within the quadrilateral.

Tangential Quadrilateral

Sides of quadrilateral: a,b,c,d
Diagonals: d1,d2
Angle between the diagonals: φ
Radius of inscribed circle: r
Perimeter: L
Semiperimeter: p
Area: S

  1. $a+c=b+d$
  2. $L=a+b+c+d=2(a+c)=2(b+d)$
  3. $r=√{d_1^2d_2^2-(a-b)^2(a+b-p)^2}/{2p},$
    where $p=L/2$
  4. $S=pr=1/2d_1d_2\ sin\ φ$

Post Tags: Geometry

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