Two tangents from a common point are congruent!
The interactive applet below will show you this rule. Just drag the points around the screen and you'll see that--no matter what--the lengths of the tangents, are always equal.
(Drawing not to scale)
Each side length that you know (5, 3, 4) is equal to the side lengths in red because they are tangent from a common point.
Since two tangents from a common point (G and H) are congruent, $$ GT = EG = 10 $$, $$ HT = HE = 10 $$.
Perimeter of quadrilateral = 10 + 10 + 10 + 10 = 40.
Since all four sides are congruent, it is a rhombus.
- YC = ZC = 21
- BZ = XB = 19
- AX = AY = 20
Perimeter = AX + AY + BZ + XB + YC + ZC = 20 + 20 + 19 + 19 + 21 + 21 = 120 .