Tangent Line To A Circle

A line tangent to a circle touches the circle at exactly ane point. The tangent line is perpendicular to the radius of the circle.

In maths problems, ane tin encounter either of two options: constructing the tangent from a point outside of the circle, or amalgam the tangent to a circle at a betoken on the circle.

1. 1

   Setup of the problem. Construct a line, tangent to the circle, passing through point ${\displaystyle P}$ .

2. 2

   Connect the point $$ P {\displaystyle P} with the centre of the circle. Yous must kickoff detect the eye of the circumvolve if information technology has not been given to yous.

3. three

   Bifurcate OP{\displaystyle OP}. The bisector intersects ${\displaystyle OP}$ in ${\displaystyle A}$ .

4. 4

   Construct a circle with radius $$ A P {\displaystyle AP} , centred at $$ A {\displaystyle A} . This circumvolve intersects the original circle at points ${\displaystyle B}$ and ${\displaystyle C}$ .

5. v

   Connect $$ P {\displaystyle P} with $$ B {\displaystyle B} or $$ C {\displaystyle C} . Both ${\displaystyle Atomic number 82}$ an ${\displaystyle PC}$ are tangent to the circumvolve.

6. vi

   Erase any structure lines, if needed.

1. 1

   Setup of the trouble. Construct a line, tangent to the circle at ${\displaystyle P}$ .

2. 2

   Describe the radius $$ M P {\displaystyle MP} . You must showtime find the centre of the circumvolve if information technology has non been given to you.

3. three

   Extend the radius past the circle.

4. 4

   Construct the perpendicular to the radius through indicate P{\displaystyle P}. That perpendicular is the tangent to the circumvolve at point ${\displaystyle P}$ .

5. v

   Erase any construction lines, if needed.

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• Question

  Why is a tangent important?

  

  Constructing a tangent makes it like shooting fish in a barrel to run into and summate the slope of a curve (such as a circle) at a given betoken.

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Tangent Line To A Circle,

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