# Two Tangents from One Point

Using Tangents to Circumscribe a Circle

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.



### Practice Problems

##### Problem 1

(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.

##### Problem 2

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.

What kind of quadrilateral is EGHT?

Since all four sides are congruent, it is a rhombus.

##### Problem 3
• YC = ZC = 21
• BZ = XB = 19
• AX = AY = 20

Perimeter = AX + AY + BZ + XB + YC + ZC = 20 + 20 + 19 + 19 + 21 + 21 = 120 .