Isosceles Trapezoid with Inscribed Circle

Posted In: Mathematics

Isosceles trapezoid with inscribed circle


Bases of Trapezoid: a,b
Leg: c
Midline: q
Altitude: h
Diagonal: D
Radius of inscribed circle: R
Radius of circumscribed circle: r
Perimeter: L
Area: S

  1. $a+b=2c$
  2. $q={a+b}/2=c$
  3. $d^2=h^2+c^2$
  4. $r=h/2=√{ab}/2$
  5. $R={cd}/{2h}={cd}/{4r}=c/2√{1+c^2/{ab}}$
    $=c/{2h}√{h^2+c^2}={a+b}/8√{a/b+6+b/a}$
  6. $L=2(a+b)=4c$
  7. $S={a+b}/2\ h={(a+b)√{ab}}/2=qh=ch={Lr}/2$

Post Tags: Geometry


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