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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.

Two tangents from 1 point

Interactive Applet (html5)

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Practice Problems

Problem 1

What is the perimeter of the triangle below?
Note: all of the segments are tangent and intersect outside the circle.

tangent to circle

(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

$$ EG = 10 \\ EH = 10 $$

  • Find the following:
  • A) GT
  • B) HT
  • C) Perimeter of quadrilateral EGTH.

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

$$ EG = 10 \\ EH = 10 $$

  • In the picture on the left, three tangents circumscribe a circle. Calculate the following lengths:
  • 1) YC
  • 2) BZ
  • 3) AX
  • 4) The perimeter of triangle ABC
  • YC = ZC = 21
  • BZ = XB = 19
  • AX = AY = 20

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


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